diff --git a/modules/dnn/test/test_backends.cpp b/modules/dnn/test/test_backends.cpp
index 19e0729abb..d1df4c35aa 100644
--- a/modules/dnn/test/test_backends.cpp
+++ b/modules/dnn/test/test_backends.cpp
@@ -248,7 +248,7 @@ TEST_P(DNNTestNetwork, MobileNet_SSD_v1_TensorFlow_Different_Width_Height)
 {
     if (backend == DNN_BACKEND_HALIDE)
         applyTestTag(CV_TEST_TAG_DNN_SKIP_HALIDE);
-#if defined(INF_ENGINE_RELEASE)
+#if defined(INF_ENGINE_RELEASE) && INF_ENGINE_VER_MAJOR_LT(2021040000)
     if ((backend == DNN_BACKEND_INFERENCE_ENGINE_NN_BUILDER_2019 || backend == DNN_BACKEND_INFERENCE_ENGINE_NGRAPH) &&
         target == DNN_TARGET_MYRIAD && getInferenceEngineVPUType() == CV_DNN_INFERENCE_ENGINE_VPU_TYPE_MYRIAD_X)
         applyTestTag(CV_TEST_TAG_DNN_SKIP_IE_MYRIAD_X);
diff --git a/modules/dnn/test/test_caffe_importer.cpp b/modules/dnn/test/test_caffe_importer.cpp
index 18b8d5ad82..7249fb4e9f 100644
--- a/modules/dnn/test/test_caffe_importer.cpp
+++ b/modules/dnn/test/test_caffe_importer.cpp
@@ -112,10 +112,12 @@ TEST(Test_Caffe, read_googlenet)
 
 TEST_P(Test_Caffe_nets, Axpy)
 {
+#if defined(INF_ENGINE_RELEASE) && INF_ENGINE_VER_MAJOR_LT(2021040000)
     if (backend == DNN_BACKEND_INFERENCE_ENGINE_NN_BUILDER_2019)
         applyTestTag(CV_TEST_TAG_DNN_SKIP_IE_NN_BUILDER);
     if (backend == DNN_BACKEND_INFERENCE_ENGINE_NGRAPH)
         applyTestTag(CV_TEST_TAG_DNN_SKIP_IE_NGRAPH);
+#endif
 
     String proto = _tf("axpy.prototxt");
     Net net = readNetFromCaffe(proto);
@@ -150,8 +152,17 @@ TEST_P(Test_Caffe_nets, Axpy)
             }
         }
     }
-    float l1 = (target == DNN_TARGET_OPENCL_FP16) ? 2e-4 : 1e-5;
-    float lInf = (target == DNN_TARGET_OPENCL_FP16) ? 1e-3 : 1e-4;
+    float l1 = 1e-5, lInf = 1e-4;
+    if (target == DNN_TARGET_OPENCL_FP16)
+    {
+        l1 = 2e-4;
+        lInf = 1e-3;
+    }
+    if (target == DNN_TARGET_MYRIAD)
+    {
+        l1 = 0.001;
+        lInf = 0.001;
+    }
     normAssert(ref, out, "", l1, lInf);
 }
 
@@ -657,7 +668,7 @@ TEST_P(Test_Caffe_nets, FasterRCNN_vgg16)
         CV_TEST_TAG_DEBUG_VERYLONG
     );
 
-#if defined(INF_ENGINE_RELEASE)
+#if defined(INF_ENGINE_RELEASE) && INF_ENGINE_VER_MAJOR_LT(2021040000)
     if ((backend == DNN_BACKEND_INFERENCE_ENGINE_NN_BUILDER_2019 || backend == DNN_BACKEND_INFERENCE_ENGINE_NGRAPH) && (target == DNN_TARGET_OPENCL || target == DNN_TARGET_OPENCL_FP16))
         applyTestTag(target == DNN_TARGET_OPENCL ? CV_TEST_TAG_DNN_SKIP_IE_OPENCL : CV_TEST_TAG_DNN_SKIP_IE_OPENCL_FP16);
 
@@ -668,6 +679,19 @@ TEST_P(Test_Caffe_nets, FasterRCNN_vgg16)
         applyTestTag(CV_TEST_TAG_DNN_SKIP_IE_MYRIAD);
 #endif
 
+#if defined(INF_ENGINE_RELEASE) && INF_ENGINE_VER_MAJOR_EQ(2021040000)
+    // IE exception: Ngraph operation Reshape with name rpn_cls_score_reshape has dynamic output shape on 0 port, but CPU plug-in supports only static shape
+    if (backend == DNN_BACKEND_INFERENCE_ENGINE_NGRAPH && (target == DNN_TARGET_OPENCL || target == DNN_TARGET_OPENCL_FP16))
+        applyTestTag(target == DNN_TARGET_OPENCL ? CV_TEST_TAG_DNN_SKIP_IE_OPENCL : CV_TEST_TAG_DNN_SKIP_IE_OPENCL_FP16,
+            CV_TEST_TAG_DNN_SKIP_IE_NGRAPH, CV_TEST_TAG_DNN_SKIP_IE_VERSION
+        );
+    // Check 'backward_compatible_check || in_out_elements_equal' failed at core/src/op/reshape.cpp:390:
+    // While validating node 'v1::Reshape bbox_pred_reshape (bbox_pred[0]:f32{1,84}, Constant_241202[0]:i64{4}) -> (f32{?,?,?,?})' with friendly_name 'bbox_pred_reshape':
+    // Requested output shape {1,6300,4,1} is incompatible with input shape Shape{1, 84}
+    if (target == DNN_TARGET_MYRIAD)
+        applyTestTag(CV_TEST_TAG_DNN_SKIP_IE_MYRIAD, CV_TEST_TAG_DNN_SKIP_IE_NGRAPH, CV_TEST_TAG_DNN_SKIP_IE_VERSION);
+#endif
+
     static Mat ref = (Mat_<float>(3, 7) << 0, 2, 0.949398, 99.2454, 210.141, 601.205, 462.849,
                                            0, 7, 0.997022, 481.841, 92.3218, 722.685, 175.953,
                                            0, 12, 0.993028, 133.221, 189.377, 350.994, 563.166);
diff --git a/modules/dnn/test/test_darknet_importer.cpp b/modules/dnn/test/test_darknet_importer.cpp
index 885bd6eb6b..f069ad190d 100644
--- a/modules/dnn/test/test_darknet_importer.cpp
+++ b/modules/dnn/test/test_darknet_importer.cpp
@@ -121,7 +121,7 @@ public:
         {
             SCOPED_TRACE("batch size 2");
 
-#if defined(INF_ENGINE_RELEASE)
+#if defined(INF_ENGINE_RELEASE) && INF_ENGINE_VER_MAJOR_LT(2021040000)
             if (target == DNN_TARGET_MYRIAD && name == "shortcut")
                 applyTestTag(CV_TEST_TAG_DNN_SKIP_IE_MYRIAD);
 #endif
@@ -429,22 +429,31 @@ TEST_P(Test_Darknet_nets_async, Accuracy)
 {
     Backend backendId = get<0>(get<1>(GetParam()));
     Target targetId = get<1>(get<1>(GetParam()));
+    std::string prefix = get<0>(GetParam());
 
+    applyTestTag(CV_TEST_TAG_MEMORY_512MB);
+
+#if defined(INF_ENGINE_RELEASE) && INF_ENGINE_VER_MAJOR_LT(2021040000)
     if (INF_ENGINE_VER_MAJOR_LT(2019020000) && backendId == DNN_BACKEND_INFERENCE_ENGINE_NN_BUILDER_2019)
         applyTestTag(CV_TEST_TAG_DNN_SKIP_IE_NN_BUILDER);
-    applyTestTag(CV_TEST_TAG_MEMORY_512MB);
 
     if (backendId == DNN_BACKEND_INFERENCE_ENGINE_NGRAPH)
         applyTestTag(CV_TEST_TAG_DNN_SKIP_IE_NGRAPH);
-
-    std::string prefix = get<0>(GetParam());
-
-    if (targetId == DNN_TARGET_MYRIAD && prefix == "yolov4")  // NC_OUT_OF_MEMORY
-        applyTestTag(CV_TEST_TAG_DNN_SKIP_IE_MYRIAD, CV_TEST_TAG_DNN_SKIP_IE_VERSION);
+#endif
 
     if (backendId != DNN_BACKEND_INFERENCE_ENGINE_NN_BUILDER_2019 && backendId != DNN_BACKEND_INFERENCE_ENGINE_NGRAPH)
         throw SkipTestException("No support for async forward");
 
+#if defined(INF_ENGINE_RELEASE)
+#if INF_ENGINE_VER_MAJOR_GE(2021040000)
+    if (targetId == DNN_TARGET_MYRIAD && prefix == "yolov3")  // NC_OUT_OF_MEMORY
+        applyTestTag(CV_TEST_TAG_DNN_SKIP_IE_MYRIAD, CV_TEST_TAG_DNN_SKIP_IE_VERSION);
+#else
+    if (targetId == DNN_TARGET_MYRIAD && prefix == "yolov4")  // NC_OUT_OF_MEMORY
+        applyTestTag(CV_TEST_TAG_DNN_SKIP_IE_MYRIAD, CV_TEST_TAG_DNN_SKIP_IE_VERSION);
+#endif
+#endif
+
     const int numInputs = 2;
     std::vector<Mat> inputs(numInputs);
     int blobSize[] = {1, 3, 416, 416};
@@ -472,6 +481,34 @@ TEST_P(Test_Darknet_nets_async, Accuracy)
     netAsync.setPreferableBackend(backendId);
     netAsync.setPreferableTarget(targetId);
 
+    double l1 = 0.0;
+    double lInf = 0.0;
+#if defined(INF_ENGINE_RELEASE)
+    if (backendId == DNN_BACKEND_INFERENCE_ENGINE_NGRAPH)
+    {
+        if (targetId == DNN_TARGET_MYRIAD && prefix == "yolo-voc")
+        {
+            l1 = 0.02;
+            lInf = 0.15;
+        }
+        if (targetId == DNN_TARGET_OPENCL_FP16 && prefix == "yolo-voc")
+        {
+            l1 = 0.02;
+            lInf = 0.1;
+        }
+        if (targetId == DNN_TARGET_OPENCL_FP16 && prefix == "yolov3")
+        {
+            l1 = 0.001;
+            lInf = 0.007;
+        }
+        if (targetId == DNN_TARGET_OPENCL_FP16 && prefix == "yolov4")
+        {
+            l1 = 0.001;
+            lInf = 0.005;
+        }
+    }
+#endif
+
     // Run asynchronously. To make test more robust, process inputs in the reversed order.
     for (int i = numInputs - 1; i >= 0; --i)
     {
@@ -481,7 +518,7 @@ TEST_P(Test_Darknet_nets_async, Accuracy)
         ASSERT_TRUE(out.valid());
         Mat result;
         EXPECT_TRUE(out.get(result, async_timeout));
-        normAssert(refs[i], result, format("Index: %d", i).c_str(), 0, 0);
+        normAssert(refs[i], result, format("Index: %d", i).c_str(), l1, lInf);
     }
 }
 
@@ -836,10 +873,23 @@ TEST_P(Test_Darknet_layers, avgpool_softmax)
 
 TEST_P(Test_Darknet_layers, region)
 {
-#if defined(INF_ENGINE_RELEASE)
-     if (backend == DNN_BACKEND_INFERENCE_ENGINE_NGRAPH && INF_ENGINE_VER_MAJOR_GE(2020020000))
-        applyTestTag(CV_TEST_TAG_DNN_SKIP_IE_NGRAPH, CV_TEST_TAG_DNN_SKIP_IE_VERSION);
+#if defined(INF_ENGINE_RELEASE) && INF_ENGINE_VER_MAJOR_LT(2021040000)
+    if (backend == DNN_BACKEND_INFERENCE_ENGINE_NGRAPH && INF_ENGINE_VER_MAJOR_GE(2020020000))
+       applyTestTag(CV_TEST_TAG_DNN_SKIP_IE_NGRAPH, CV_TEST_TAG_DNN_SKIP_IE_VERSION);
 #endif
+
+#if defined(INF_ENGINE_RELEASE) && INF_ENGINE_VER_MAJOR_EQ(2021040000)
+    // accuracy on CPU, OpenCL
+    // Expected: (normInf) <= (lInf), actual: 0.763223 vs 0.0001
+    //   |ref| = 1.207319974899292
+    if (backend == DNN_BACKEND_INFERENCE_ENGINE_NGRAPH && target == DNN_TARGET_CPU)
+        applyTestTag(CV_TEST_TAG_DNN_SKIP_IE_CPU, CV_TEST_TAG_DNN_SKIP_IE_NGRAPH, CV_TEST_TAG_DNN_SKIP_IE_VERSION);
+    if (backend == DNN_BACKEND_INFERENCE_ENGINE_NGRAPH && (target == DNN_TARGET_OPENCL || target == DNN_TARGET_OPENCL_FP16))
+        applyTestTag(target == DNN_TARGET_OPENCL ? CV_TEST_TAG_DNN_SKIP_IE_OPENCL : CV_TEST_TAG_DNN_SKIP_IE_OPENCL_FP16,
+            CV_TEST_TAG_DNN_SKIP_IE_NGRAPH, CV_TEST_TAG_DNN_SKIP_IE_VERSION
+        );
+#endif
+
     testDarknetLayer("region");
 }
 
diff --git a/modules/dnn/test/test_halide_layers.cpp b/modules/dnn/test/test_halide_layers.cpp
index b24968b8e8..405587eec7 100644
--- a/modules/dnn/test/test_halide_layers.cpp
+++ b/modules/dnn/test/test_halide_layers.cpp
@@ -240,9 +240,11 @@ TEST_P(LRN, Accuracy)
     Backend backendId = get<0>(get<5>(GetParam()));
     Target targetId = get<1>(get<5>(GetParam()));
 
+#if defined(INF_ENGINE_RELEASE) && INF_ENGINE_VER_MAJOR_LT(2021040000)
     if ((inSize.width == 5 || inSize.height == 5) && targetId == DNN_TARGET_MYRIAD &&
         nrmType == "ACROSS_CHANNELS")
         applyTestTag(CV_TEST_TAG_DNN_SKIP_IE_MYRIAD);
+#endif
 
     LayerParams lp;
     lp.set("norm_region", nrmType);
@@ -407,12 +409,14 @@ TEST_P(FullyConnected, Accuracy)
     bool hasBias = get<3>(GetParam());
     Backend backendId = get<0>(get<4>(GetParam()));
     Target targetId = get<1>(get<4>(GetParam()));
+#if defined(INF_ENGINE_RELEASE) && INF_ENGINE_VER_MAJOR_LT(2021040000)
     if ((backendId == DNN_BACKEND_INFERENCE_ENGINE_NN_BUILDER_2019 ||
          backendId == DNN_BACKEND_INFERENCE_ENGINE_NGRAPH) && (targetId == DNN_TARGET_OPENCL_FP16 ||
        (targetId == DNN_TARGET_MYRIAD && getInferenceEngineVPUType() == CV_DNN_INFERENCE_ENGINE_VPU_TYPE_MYRIAD_X))) {
         applyTestTag(CV_TEST_TAG_DNN_SKIP_IE_OPENCL_FP16);
         applyTestTag(CV_TEST_TAG_DNN_SKIP_IE_MYRIAD_X);
     }
+#endif
 
     Mat weights(outChannels, inChannels * inSize.height * inSize.width, CV_32F);
     randu(weights, -1.0f, 1.0f);
@@ -430,7 +434,21 @@ TEST_P(FullyConnected, Accuracy)
 
     int sz[] = {1, inChannels, inSize.height, inSize.width};
     Mat input(4, &sz[0], CV_32F);
-    test(lp, input, backendId, targetId);
+
+    double l1 = 0.0;
+    double lInf = 0.0;
+#if defined(INF_ENGINE_RELEASE)
+    if (targetId == DNN_TARGET_MYRIAD)
+    {
+        l1 = 0.015;
+        lInf = 0.025;
+    }
+    else if (backendId == DNN_BACKEND_INFERENCE_ENGINE_NGRAPH && targetId == DNN_TARGET_OPENCL_FP16)
+    {
+        l1 = 0.01;
+    }
+#endif
+    test(lp, input, backendId, targetId, false, l1, lInf);
 }
 
 INSTANTIATE_TEST_CASE_P(Layer_Test_Halide, FullyConnected, Combine(
@@ -812,18 +830,18 @@ TEST_P(Eltwise, Accuracy)
         applyTestTag(CV_TEST_TAG_DNN_SKIP_IE_MYRIAD, CV_TEST_TAG_DNN_SKIP_IE_NN_BUILDER, CV_TEST_TAG_DNN_SKIP_IE_VERSION);
 #endif
 
-#if defined(INF_ENGINE_RELEASE) && INF_ENGINE_VER_MAJOR_GE(2019010000)
+#if defined(INF_ENGINE_RELEASE) && INF_ENGINE_VER_MAJOR_GE(2019010000) && INF_ENGINE_VER_MAJOR_LT(2021040000)
     if (backendId == DNN_BACKEND_INFERENCE_ENGINE_NN_BUILDER_2019 && numConv > 1)
         applyTestTag(CV_TEST_TAG_DNN_SKIP_IE_NN_BUILDER, CV_TEST_TAG_DNN_SKIP_IE_VERSION);
 #endif
 
-#if defined(INF_ENGINE_RELEASE)
+#if defined(INF_ENGINE_RELEASE) && INF_ENGINE_VER_MAJOR_LT(2021040000)
     if (backendId == DNN_BACKEND_INFERENCE_ENGINE_NN_BUILDER_2019 && targetId == DNN_TARGET_OPENCL &&
         op == "sum" && numConv == 1 && !weighted)
         applyTestTag(CV_TEST_TAG_DNN_SKIP_IE_OPENCL, CV_TEST_TAG_DNN_SKIP_IE_NN_BUILDER);
 #endif
 
-#if defined(INF_ENGINE_RELEASE)
+#if defined(INF_ENGINE_RELEASE) && INF_ENGINE_VER_MAJOR_LT(2021040000)
     if (backendId == DNN_BACKEND_INFERENCE_ENGINE_NGRAPH && numConv > 1)
         applyTestTag(CV_TEST_TAG_DNN_SKIP_IE_NGRAPH, CV_TEST_TAG_DNN_SKIP_IE_VERSION);
 #endif
diff --git a/modules/dnn/test/test_layers.cpp b/modules/dnn/test/test_layers.cpp
index e61fd733f9..2d4f78c88c 100644
--- a/modules/dnn/test/test_layers.cpp
+++ b/modules/dnn/test/test_layers.cpp
@@ -194,13 +194,23 @@ TEST_P(Test_Caffe_layers, DeConvolution)
 
 TEST_P(Test_Caffe_layers, InnerProduct)
 {
+#if defined(INF_ENGINE_RELEASE) && INF_ENGINE_VER_MAJOR_LT(2021040000)
     if (backend == DNN_BACKEND_INFERENCE_ENGINE_NN_BUILDER_2019)
         applyTestTag(CV_TEST_TAG_DNN_SKIP_IE_NN_BUILDER);
     if (backend == DNN_BACKEND_INFERENCE_ENGINE_NGRAPH)
         applyTestTag(CV_TEST_TAG_DNN_SKIP_IE_NGRAPH);
+#endif
+#if defined(INF_ENGINE_RELEASE) && INF_ENGINE_VER_MAJOR_EQ(2021040000)
+    // IE exception: Ngraph operation Reshape with name Reshape_4219609 has dynamic output shape on 0 port, but CPU plug-in supports only static shape
+    if (backend == DNN_BACKEND_INFERENCE_ENGINE_NGRAPH && (target == DNN_TARGET_OPENCL || target == DNN_TARGET_OPENCL_FP16))
+        applyTestTag(target == DNN_TARGET_OPENCL ? CV_TEST_TAG_DNN_SKIP_IE_OPENCL : CV_TEST_TAG_DNN_SKIP_IE_OPENCL_FP16,
+            CV_TEST_TAG_DNN_SKIP_IE_NGRAPH, CV_TEST_TAG_DNN_SKIP_IE_VERSION
+        );
+#endif
 
     if (backend == DNN_BACKEND_OPENCV && target == DNN_TARGET_OPENCL_FP16)
         applyTestTag(CV_TEST_TAG_DNN_SKIP_OPENCL_FP16);
+
     testLayerUsingCaffeModels("layer_inner_product", true);
 }
 
@@ -295,10 +305,12 @@ TEST_P(Test_Caffe_layers, Concat)
                      CV_TEST_TAG_DNN_SKIP_IE_NN_BUILDER, CV_TEST_TAG_DNN_SKIP_IE_VERSION);
 #endif
 
+#if INF_ENGINE_VER_MAJOR_LT(2021040000)
     if (backend == DNN_BACKEND_INFERENCE_ENGINE_NGRAPH &&
         (target == DNN_TARGET_OPENCL || target == DNN_TARGET_OPENCL_FP16))
         applyTestTag(target == DNN_TARGET_OPENCL ? CV_TEST_TAG_DNN_SKIP_IE_OPENCL : CV_TEST_TAG_DNN_SKIP_IE_OPENCL_FP16,
                      CV_TEST_TAG_DNN_SKIP_IE_NGRAPH, CV_TEST_TAG_DNN_SKIP_IE_VERSION);
+#endif
 
 #endif
     testLayerUsingCaffeModels("layer_concat");
diff --git a/modules/dnn/test/test_misc.cpp b/modules/dnn/test/test_misc.cpp
index 9971450478..0de503ac7d 100644
--- a/modules/dnn/test/test_misc.cpp
+++ b/modules/dnn/test/test_misc.cpp
@@ -578,7 +578,8 @@ TEST_P(Async, create_layer_pipeline_set_and_forward_all)
     if (backendId != DNN_BACKEND_INFERENCE_ENGINE_NN_BUILDER_2019 && backendId != DNN_BACKEND_INFERENCE_ENGINE_NGRAPH)
         throw SkipTestException("No support for async forward");
 
-    if (backendId == DNN_BACKEND_INFERENCE_ENGINE_NGRAPH)
+    // Exception: Default implementation fallbacks in asynchronous mode
+    if (backendId == DNN_BACKEND_INFERENCE_ENGINE_NGRAPH && dtype == CV_8U)
         applyTestTag(CV_TEST_TAG_DNN_SKIP_IE_NGRAPH);
 
     if (backendId == DNN_BACKEND_INFERENCE_ENGINE_NN_BUILDER_2019)
diff --git a/modules/dnn/test/test_onnx_importer.cpp b/modules/dnn/test/test_onnx_importer.cpp
index 0fd5d08258..a432f2251e 100644
--- a/modules/dnn/test/test_onnx_importer.cpp
+++ b/modules/dnn/test/test_onnx_importer.cpp
@@ -185,17 +185,11 @@ TEST_P(Test_ONNX_layers, Gather)
 
 TEST_P(Test_ONNX_layers, Convolution3D)
 {
-#if defined(INF_ENGINE_RELEASE) && INF_ENGINE_VER_MAJOR_LT(2019010000)
-    applyTestTag(CV_TEST_TAG_DNN_SKIP_IE_VERSION);
-#endif
     testONNXModels("conv3d");
 }
 
 TEST_P(Test_ONNX_layers, Convolution3D_bias)
 {
-#if defined(INF_ENGINE_RELEASE) && INF_ENGINE_VER_MAJOR_LT(2019010000)
-    applyTestTag(CV_TEST_TAG_DNN_SKIP_IE_VERSION);
-#endif
     testONNXModels("conv3d_bias");
 }
 
@@ -222,14 +216,73 @@ TEST_P(Test_ONNX_layers, Deconvolution)
 
 TEST_P(Test_ONNX_layers, Deconvolution3D)
 {
-#if defined(INF_ENGINE_RELEASE) && INF_ENGINE_VER_MAJOR_EQ(2018050000)
-    applyTestTag(CV_TEST_TAG_DNN_SKIP_IE_VERSION);
+#if defined(INF_ENGINE_RELEASE) && INF_ENGINE_VER_MAJOR_EQ(2021040000)
+    if (backend == DNN_BACKEND_INFERENCE_ENGINE_NGRAPH)
+    {
+        // [ GENERAL_ERROR ] vpu/graph_transformer/src/frontend/frontend.cpp:439 Failed to compile layer "2":
+        // [ GENERAL_ERROR ] vpu/graph_transformer/src/model/model.cpp:198 duplicateData error: while duplicating 2@weights Const data got different desc and content byte sizes (162 and 486 respectively)
+        if (target == DNN_TARGET_MYRIAD)
+            applyTestTag(CV_TEST_TAG_DNN_SKIP_IE_MYRIAD, CV_TEST_TAG_DNN_SKIP_IE_NGRAPH, CV_TEST_TAG_DNN_SKIP_IE_VERSION);
+    }
 #endif
-    if (backend == DNN_BACKEND_OPENCV || target != DNN_TARGET_CPU)
-        throw SkipTestException("Only DLIE backend on CPU is supported");
+
+    if (backend == DNN_BACKEND_OPENCV)
+        throw SkipTestException("OpenCV backend is not supported");  // FIXIT use tags
+
     testONNXModels("deconv3d");
+}
+
+TEST_P(Test_ONNX_layers, Deconvolution3D_bias)
+{
+#if defined(INF_ENGINE_RELEASE) && INF_ENGINE_VER_MAJOR_EQ(2021040000)
+    if (backend == DNN_BACKEND_INFERENCE_ENGINE_NGRAPH)
+    {
+        // [ GENERAL_ERROR ] vpu/graph_transformer/src/frontend/frontend.cpp:439 Failed to compile layer "2":
+        // [ GENERAL_ERROR ] vpu/graph_transformer/src/model/model.cpp:198 duplicateData error: while duplicating 2@weights Const data got different desc and content byte sizes (162 and 486 respectively)
+        if (target == DNN_TARGET_MYRIAD)
+            applyTestTag(CV_TEST_TAG_DNN_SKIP_IE_MYRIAD, CV_TEST_TAG_DNN_SKIP_IE_NGRAPH, CV_TEST_TAG_DNN_SKIP_IE_VERSION);
+    }
+#endif
+
+    if (backend == DNN_BACKEND_OPENCV)
+        throw SkipTestException("OpenCV backend is not supported");  // FIXIT use tags
+
     testONNXModels("deconv3d_bias");
+}
+
+TEST_P(Test_ONNX_layers, Deconvolution3D_pad)
+{
+#if defined(INF_ENGINE_RELEASE) && INF_ENGINE_VER_MAJOR_EQ(2021040000)
+    if (backend == DNN_BACKEND_INFERENCE_ENGINE_NGRAPH)
+    {
+        // [ GENERAL_ERROR ] vpu/graph_transformer/src/frontend/frontend.cpp:439 Failed to compile layer "2":
+        // [ GENERAL_ERROR ] vpu/graph_transformer/src/model/model.cpp:198 duplicateData error: while duplicating 2@weights Const data got different desc and content byte sizes (162 and 486 respectively)
+        if (target == DNN_TARGET_MYRIAD)
+            applyTestTag(CV_TEST_TAG_DNN_SKIP_IE_MYRIAD, CV_TEST_TAG_DNN_SKIP_IE_NGRAPH, CV_TEST_TAG_DNN_SKIP_IE_VERSION);
+    }
+#endif
+
+    if (backend == DNN_BACKEND_OPENCV)
+        throw SkipTestException("OpenCV backend is not supported");  // FIXIT use tags
+
     testONNXModels("deconv3d_pad");
+}
+
+TEST_P(Test_ONNX_layers, Deconvolution3D_adjpad)
+{
+#if defined(INF_ENGINE_RELEASE) && INF_ENGINE_VER_MAJOR_EQ(2021040000)
+    if (backend == DNN_BACKEND_INFERENCE_ENGINE_NGRAPH)
+    {
+        // [ GENERAL_ERROR ] vpu/graph_transformer/src/frontend/frontend.cpp:439 Failed to compile layer "2":
+        // [ GENERAL_ERROR ] vpu/graph_transformer/src/model/model.cpp:198 duplicateData error: while duplicating 2@weights Const data got different desc and content byte sizes (162 and 486 respectively)
+        if (target == DNN_TARGET_MYRIAD)
+            applyTestTag(CV_TEST_TAG_DNN_SKIP_IE_MYRIAD, CV_TEST_TAG_DNN_SKIP_IE_NGRAPH, CV_TEST_TAG_DNN_SKIP_IE_VERSION);
+    }
+#endif
+
+    if (backend == DNN_BACKEND_OPENCV)
+        throw SkipTestException("OpenCV backend is not supported");  // FIXIT use tags
+
     testONNXModels("deconv3d_adjpad");
 }
 
@@ -295,12 +348,15 @@ TEST_P(Test_ONNX_layers, Scale)
 
 TEST_P(Test_ONNX_layers, ReduceMean3D)
 {
+#if defined(INF_ENGINE_RELEASE) && INF_ENGINE_VER_MAJOR_LT(2021040000)
     if (backend == DNN_BACKEND_INFERENCE_ENGINE_NN_BUILDER_2019 && target != DNN_TARGET_CPU)
         applyTestTag(CV_TEST_TAG_DNN_SKIP_IE_NN_BUILDER);  // Only CPU on DLIE backend is supported
     if (backend == DNN_BACKEND_INFERENCE_ENGINE_NGRAPH && target != DNN_TARGET_CPU)
         applyTestTag(CV_TEST_TAG_DNN_SKIP_IE_NGRAPH);  // Only CPU on DLIE backend is supported
-    if (target != DNN_TARGET_CPU)
-        throw SkipTestException("Only CPU is supported");
+#endif
+    if (backend == DNN_BACKEND_OPENCV && target != DNN_TARGET_CPU)
+        throw SkipTestException("Only CPU is supported");  // FIXIT use tags
+
     testONNXModels("reduce_mean3d");
 }
 
@@ -340,13 +396,12 @@ TEST_P(Test_ONNX_layers, Concatenation)
 
 TEST_P(Test_ONNX_layers, Eltwise3D)
 {
-#if defined(INF_ENGINE_RELEASE) && INF_ENGINE_VER_MAJOR_LT(2019010000)
-    applyTestTag(CV_TEST_TAG_DNN_SKIP_IE_VERSION);
-#endif
+#if defined(INF_ENGINE_RELEASE) && INF_ENGINE_VER_MAJOR_LT(2021040000)
     if (backend == DNN_BACKEND_INFERENCE_ENGINE_NN_BUILDER_2019 && target != DNN_TARGET_CPU)
         applyTestTag(CV_TEST_TAG_DNN_SKIP_IE_NN_BUILDER);  // Only CPU on DLIE backend is supported
     if (backend == DNN_BACKEND_INFERENCE_ENGINE_NGRAPH && target != DNN_TARGET_CPU)
         applyTestTag(CV_TEST_TAG_DNN_SKIP_IE_NGRAPH);  // Only CPU on DLIE backend is supported
+#endif
     testONNXModels("eltwise3d");
 }
 
@@ -357,43 +412,56 @@ TEST_P(Test_ONNX_layers, AveragePooling)
 
 TEST_P(Test_ONNX_layers, MaxPooling3D)
 {
-#if defined(INF_ENGINE_RELEASE) && INF_ENGINE_VER_MAJOR_LT(2019010000)
-    applyTestTag(CV_TEST_TAG_DNN_SKIP_IE_VERSION);
+#if defined(INF_ENGINE_RELEASE) && INF_ENGINE_VER_MAJOR_EQ(2021040000)
+    if (backend == DNN_BACKEND_INFERENCE_ENGINE_NGRAPH)
+    {
+        // accuracy
+        if (target == DNN_TARGET_OPENCL || target == DNN_TARGET_OPENCL_FP16)
+            applyTestTag(target == DNN_TARGET_OPENCL ? CV_TEST_TAG_DNN_SKIP_IE_OPENCL : CV_TEST_TAG_DNN_SKIP_IE_OPENCL_FP16,
+                CV_TEST_TAG_DNN_SKIP_IE_NGRAPH, CV_TEST_TAG_DNN_SKIP_IE_VERSION
+            );
+        // IE exception: [ GENERAL_ERROR ]  AssertionFailed: !expired()
+        if (target == DNN_TARGET_MYRIAD)
+            applyTestTag(CV_TEST_TAG_DNN_SKIP_IE_MYRIAD, CV_TEST_TAG_DNN_SKIP_IE_NGRAPH, CV_TEST_TAG_DNN_SKIP_IE_VERSION);
+    }
 #endif
+#if defined(INF_ENGINE_RELEASE) && INF_ENGINE_VER_MAJOR_LT(2021040000)
     if (backend == DNN_BACKEND_INFERENCE_ENGINE_NN_BUILDER_2019 && target != DNN_TARGET_CPU)
         applyTestTag(CV_TEST_TAG_DNN_SKIP_IE_NN_BUILDER);  // Only CPU on DLIE backend is supported
     if (backend == DNN_BACKEND_INFERENCE_ENGINE_NGRAPH && target != DNN_TARGET_CPU)
         applyTestTag(CV_TEST_TAG_DNN_SKIP_IE_NGRAPH);  // Only CPU on DLIE backend is supported
-    if (target != DNN_TARGET_CPU)
-        throw SkipTestException("Only CPU is supported");
+#endif
+    if (backend == DNN_BACKEND_OPENCV && target != DNN_TARGET_CPU)
+        throw SkipTestException("Only CPU is supported");  // FIXIT use tags
+
     testONNXModels("max_pool3d", npy, 0, 0, false, false);
 }
 
 TEST_P(Test_ONNX_layers, AvePooling3D)
 {
-#if defined(INF_ENGINE_RELEASE) && INF_ENGINE_VER_MAJOR_LT(2019010000)
-    applyTestTag(CV_TEST_TAG_DNN_SKIP_IE_VERSION);
-#endif
+#if defined(INF_ENGINE_RELEASE) && INF_ENGINE_VER_MAJOR_LT(2021040000)
     if (backend == DNN_BACKEND_INFERENCE_ENGINE_NN_BUILDER_2019 && target != DNN_TARGET_CPU)
         applyTestTag(CV_TEST_TAG_DNN_SKIP_IE_NN_BUILDER);  // Only CPU on DLIE backend is supported
     if (backend == DNN_BACKEND_INFERENCE_ENGINE_NGRAPH && target != DNN_TARGET_CPU)
         applyTestTag(CV_TEST_TAG_DNN_SKIP_IE_NGRAPH);  // Only CPU on DLIE backend is supported
-    if (target != DNN_TARGET_CPU)
-        throw SkipTestException("Only CPU is supported");
+#endif
+    if (backend == DNN_BACKEND_OPENCV && target != DNN_TARGET_CPU)
+        throw SkipTestException("Only CPU is supported");  // FIXIT use tags
+
     testONNXModels("ave_pool3d");
 }
 
 TEST_P(Test_ONNX_layers, PoolConv3D)
 {
-#if defined(INF_ENGINE_RELEASE) && INF_ENGINE_VER_MAJOR_LT(2019010000)
-    applyTestTag(CV_TEST_TAG_DNN_SKIP_IE_VERSION);
-#endif
+#if defined(INF_ENGINE_RELEASE) && INF_ENGINE_VER_MAJOR_LT(2021040000)
     if (backend == DNN_BACKEND_INFERENCE_ENGINE_NN_BUILDER_2019 && target != DNN_TARGET_CPU)
         applyTestTag(CV_TEST_TAG_DNN_SKIP_IE_NN_BUILDER);  // Only CPU on DLIE backend is supported
     if (backend == DNN_BACKEND_INFERENCE_ENGINE_NGRAPH && target != DNN_TARGET_CPU)
         applyTestTag(CV_TEST_TAG_DNN_SKIP_IE_NGRAPH);  // Only CPU on DLIE backend is supported
-    if (target != DNN_TARGET_CPU)
-        throw SkipTestException("Only CPU is supported");
+#endif
+    if (backend == DNN_BACKEND_OPENCV && target != DNN_TARGET_CPU)
+        throw SkipTestException("Only CPU is supported");  // FIXIT use tags
+
     testONNXModels("pool_conv_3d");
 }
 
@@ -875,6 +943,7 @@ TEST_P(Test_ONNX_layers, DynamicAxes)
 
 TEST_P(Test_ONNX_layers, MaxPool1d)
 {
+#if defined(INF_ENGINE_RELEASE) && INF_ENGINE_VER_MAJOR_LT(2021040000)
     if (backend == DNN_BACKEND_INFERENCE_ENGINE_NN_BUILDER_2019)
     {
         if (target == DNN_TARGET_MYRIAD) applyTestTag(CV_TEST_TAG_DNN_SKIP_IE_MYRIAD, CV_TEST_TAG_DNN_SKIP_IE_NN_BUILDER);
@@ -883,11 +952,20 @@ TEST_P(Test_ONNX_layers, MaxPool1d)
     {
         if (target == DNN_TARGET_MYRIAD) applyTestTag(CV_TEST_TAG_DNN_SKIP_IE_MYRIAD, CV_TEST_TAG_DNN_SKIP_IE_NGRAPH);
     }
+#endif
+#if defined(INF_ENGINE_RELEASE) && INF_ENGINE_VER_MAJOR_GE(2021040000)
+    if (backend == DNN_BACKEND_INFERENCE_ENGINE_NGRAPH && target == DNN_TARGET_MYRIAD)
+    {
+        // 2021.4: [ GENERAL_ERROR ]  AssertionFailed: !expired()
+        applyTestTag(CV_TEST_TAG_DNN_SKIP_IE_MYRIAD, CV_TEST_TAG_DNN_SKIP_IE_NGRAPH);
+    }
+#endif
     testONNXModels("maxpooling_1d");
 }
 
 TEST_P(Test_ONNX_layers, MaxPoolSigmoid1d)
 {
+#if defined(INF_ENGINE_RELEASE) && INF_ENGINE_VER_MAJOR_LT(2021040000)
     if (backend == DNN_BACKEND_INFERENCE_ENGINE_NN_BUILDER_2019)
     {
         if (target == DNN_TARGET_MYRIAD) applyTestTag(CV_TEST_TAG_DNN_SKIP_IE_MYRIAD, CV_TEST_TAG_DNN_SKIP_IE_NN_BUILDER);
@@ -896,11 +974,13 @@ TEST_P(Test_ONNX_layers, MaxPoolSigmoid1d)
     {
         if (target == DNN_TARGET_MYRIAD) applyTestTag(CV_TEST_TAG_DNN_SKIP_IE_MYRIAD, CV_TEST_TAG_DNN_SKIP_IE_NGRAPH);
     }
+#endif
     testONNXModels("maxpooling_sigmoid_1d");
 }
 
 TEST_P(Test_ONNX_layers, MaxPool1d_Twise)
 {
+#if defined(INF_ENGINE_RELEASE) && INF_ENGINE_VER_MAJOR_LT(2021040000)
     if (backend == DNN_BACKEND_INFERENCE_ENGINE_NN_BUILDER_2019)
     {
         if (target == DNN_TARGET_MYRIAD) applyTestTag(CV_TEST_TAG_DNN_SKIP_IE_MYRIAD, CV_TEST_TAG_DNN_SKIP_IE_NN_BUILDER);
@@ -909,11 +989,13 @@ TEST_P(Test_ONNX_layers, MaxPool1d_Twise)
     {
         if (target == DNN_TARGET_MYRIAD) applyTestTag(CV_TEST_TAG_DNN_SKIP_IE_MYRIAD, CV_TEST_TAG_DNN_SKIP_IE_NGRAPH);
     }
+#endif
     testONNXModels("two_maxpooling_1d");
 }
 
 TEST_P(Test_ONNX_layers, AvePool1d)
 {
+#if defined(INF_ENGINE_RELEASE) && INF_ENGINE_VER_MAJOR_LT(2021040000)
     if (backend == DNN_BACKEND_INFERENCE_ENGINE_NN_BUILDER_2019)
     {
         if (target == DNN_TARGET_MYRIAD) applyTestTag(CV_TEST_TAG_DNN_SKIP_IE_MYRIAD, CV_TEST_TAG_DNN_SKIP_IE_NN_BUILDER);
@@ -922,11 +1004,13 @@ TEST_P(Test_ONNX_layers, AvePool1d)
     {
         if (target == DNN_TARGET_MYRIAD) applyTestTag(CV_TEST_TAG_DNN_SKIP_IE_MYRIAD, CV_TEST_TAG_DNN_SKIP_IE_NGRAPH);
     }
+#endif
     testONNXModels("average_pooling_1d");
 }
 
 TEST_P(Test_ONNX_layers, PoolConv1d)
 {
+#if defined(INF_ENGINE_RELEASE) && INF_ENGINE_VER_MAJOR_LT(2021040000)
     if (backend == DNN_BACKEND_INFERENCE_ENGINE_NN_BUILDER_2019)
     {
         if (target == DNN_TARGET_MYRIAD) applyTestTag(CV_TEST_TAG_DNN_SKIP_IE_MYRIAD, CV_TEST_TAG_DNN_SKIP_IE_NN_BUILDER);
@@ -935,6 +1019,7 @@ TEST_P(Test_ONNX_layers, PoolConv1d)
     {
         if (target == DNN_TARGET_MYRIAD) applyTestTag(CV_TEST_TAG_DNN_SKIP_IE_MYRIAD, CV_TEST_TAG_DNN_SKIP_IE_NGRAPH);
     }
+#endif
     testONNXModels("pool_conv_1d");
 }
 
@@ -1014,11 +1099,18 @@ TEST_P(Test_ONNX_nets, Squeezenet)
 
 TEST_P(Test_ONNX_nets, Googlenet)
 {
+#if defined(INF_ENGINE_RELEASE) && INF_ENGINE_VER_MAJOR_LT(2021040000)
     if (backend == DNN_BACKEND_INFERENCE_ENGINE_NN_BUILDER_2019)
         applyTestTag(CV_TEST_TAG_DNN_SKIP_IE_NN_BUILDER);
 
     if (backend == DNN_BACKEND_INFERENCE_ENGINE_NGRAPH)
         applyTestTag(CV_TEST_TAG_DNN_SKIP_IE_NGRAPH);
+#endif
+#if defined(INF_ENGINE_RELEASE) && INF_ENGINE_VER_MAJOR_EQ(2021040000)
+    // accuracy
+    if (target == DNN_TARGET_MYRIAD)
+        applyTestTag(CV_TEST_TAG_DNN_SKIP_IE_MYRIAD, CV_TEST_TAG_DNN_SKIP_IE_NGRAPH, CV_TEST_TAG_DNN_SKIP_IE_VERSION);
+#endif
 
     const String model = _tf("models/googlenet.onnx", false);
 
@@ -1264,7 +1356,7 @@ TEST_P(Test_ONNX_nets, DenseNet121)
 
 TEST_P(Test_ONNX_nets, Inception_v1)
 {
-#if defined(INF_ENGINE_RELEASE)
+#if defined(INF_ENGINE_RELEASE) && INF_ENGINE_VER_MAJOR_LT(2021040000)
     if ((backend == DNN_BACKEND_INFERENCE_ENGINE_NN_BUILDER_2019 ||
          backend == DNN_BACKEND_INFERENCE_ENGINE_NGRAPH) && target == DNN_TARGET_MYRIAD)
         applyTestTag(CV_TEST_TAG_DNN_SKIP_IE_MYRIAD);
@@ -1274,26 +1366,35 @@ TEST_P(Test_ONNX_nets, Inception_v1)
 
 TEST_P(Test_ONNX_nets, Shufflenet)
 {
+#if defined(INF_ENGINE_RELEASE) && INF_ENGINE_VER_MAJOR_LT(2021040000)
     if (backend == DNN_BACKEND_INFERENCE_ENGINE_NN_BUILDER_2019)
     {
         if (target == DNN_TARGET_OPENCL_FP16) applyTestTag(CV_TEST_TAG_DNN_SKIP_IE_OPENCL_FP16, CV_TEST_TAG_DNN_SKIP_IE_NN_BUILDER);
         if (target == DNN_TARGET_OPENCL)      applyTestTag(CV_TEST_TAG_DNN_SKIP_IE_OPENCL, CV_TEST_TAG_DNN_SKIP_IE_NN_BUILDER);
         if (target == DNN_TARGET_MYRIAD)      applyTestTag(CV_TEST_TAG_DNN_SKIP_IE_MYRIAD, CV_TEST_TAG_DNN_SKIP_IE_NN_BUILDER);
     }
+#endif
     testONNXModels("shufflenet", pb);
 }
 
 TEST_P(Test_ONNX_nets, Resnet34_kinetics)
 {
-#if defined(INF_ENGINE_RELEASE) && INF_ENGINE_VER_MAJOR_LT(2019010000)
-    applyTestTag(CV_TEST_TAG_DNN_SKIP_IE_VERSION);
-#endif
+#if defined(INF_ENGINE_RELEASE) && INF_ENGINE_VER_MAJOR_LT(2021040000)
     if (backend == DNN_BACKEND_INFERENCE_ENGINE_NN_BUILDER_2019 && target != DNN_TARGET_CPU)
         applyTestTag(CV_TEST_TAG_DNN_SKIP_IE_NN_BUILDER);  // Only CPU on DLIE backend is supported
     if (backend == DNN_BACKEND_INFERENCE_ENGINE_NGRAPH && target != DNN_TARGET_CPU)
         applyTestTag(CV_TEST_TAG_DNN_SKIP_IE_NGRAPH);  // Only CPU on DLIE backend is supported
-    if (target != DNN_TARGET_CPU)
-        throw SkipTestException("Only CPU is supported");
+#endif
+#if defined(INF_ENGINE_RELEASE) && INF_ENGINE_VER_MAJOR_EQ(2021040000)
+    if (backend == DNN_BACKEND_INFERENCE_ENGINE_NGRAPH)
+    {
+        // IE exception: Function contains several inputs and outputs with one friendly name!
+        if (target == DNN_TARGET_MYRIAD)
+            applyTestTag(CV_TEST_TAG_DNN_SKIP_IE_MYRIAD, CV_TEST_TAG_DNN_SKIP_IE_NGRAPH, CV_TEST_TAG_DNN_SKIP_IE_VERSION);
+    }
+#endif
+    if (backend == DNN_BACKEND_OPENCV && target != DNN_TARGET_CPU)
+        throw SkipTestException("Only CPU is supported");  // FIXIT use tags
 
     String onnxmodel = findDataFile("dnn/resnet-34_kinetics.onnx", false);
     Mat image0 = imread(findDataFile("dnn/dog416.png"));
@@ -1334,6 +1435,11 @@ TEST_P(Test_ONNX_nets, Resnet34_kinetics)
     // output range [-5, 11]
     float l1 = 0.0013;
     float lInf = 0.009;
+    if (backend == DNN_BACKEND_INFERENCE_ENGINE_NGRAPH && target == DNN_TARGET_OPENCL_FP16)
+    {
+        l1 = 0.02;
+        lInf = 0.07;
+    }
 
     checkBackend(&input0, &ref0);
     net.setInput(input0);
diff --git a/modules/dnn/test/test_tf_importer.cpp b/modules/dnn/test/test_tf_importer.cpp
index d02b7136d6..073a2f3395 100644
--- a/modules/dnn/test/test_tf_importer.cpp
+++ b/modules/dnn/test/test_tf_importer.cpp
@@ -215,13 +215,12 @@ TEST_P(Test_TensorFlow_layers, conv_pool_nchw)
 
 TEST_P(Test_TensorFlow_layers, Convolution3D)
 {
-#if defined(INF_ENGINE_RELEASE) && INF_ENGINE_VER_MAJOR_LT(2019010000)
-    applyTestTag(CV_TEST_TAG_DNN_SKIP_IE_VERSION);
-#endif
+#if defined(INF_ENGINE_RELEASE) && INF_ENGINE_VER_MAJOR_LT(2021040000)
     if (backend == DNN_BACKEND_INFERENCE_ENGINE_NN_BUILDER_2019 && target != DNN_TARGET_CPU)
         applyTestTag(CV_TEST_TAG_DNN_SKIP_IE_NN_BUILDER);  // Only CPU on DLIE backend is supported
     if (backend == DNN_BACKEND_INFERENCE_ENGINE_NGRAPH && target != DNN_TARGET_CPU)
         applyTestTag(CV_TEST_TAG_DNN_SKIP_IE_NGRAPH);  // Only CPU on DLIE backend is supported
+#endif
     runTensorFlowNet("conv3d");
 }
 
@@ -230,7 +229,7 @@ TEST_P(Test_TensorFlow_layers, padding)
     runTensorFlowNet("padding_valid");
     runTensorFlowNet("spatial_padding");
     runTensorFlowNet("mirror_pad");
-#if defined(INF_ENGINE_RELEASE) && INF_ENGINE_VER_MAJOR_GE(2019020000)
+#if defined(INF_ENGINE_RELEASE) && INF_ENGINE_VER_MAJOR_GE(2019020000) && INF_ENGINE_VER_MAJOR_LT(2021040000)
     if (target == DNN_TARGET_MYRIAD)
     {
         if (backend == DNN_BACKEND_INFERENCE_ENGINE_NN_BUILDER_2019)
@@ -343,6 +342,7 @@ TEST_P(Test_TensorFlow_layers, concat_axis_1)
 
 TEST_P(Test_TensorFlow_layers, concat_3d)
 {
+#if defined(INF_ENGINE_RELEASE) && INF_ENGINE_VER_MAJOR_LT(2021040000)
     if (backend == DNN_BACKEND_OPENCV && target != DNN_TARGET_CPU)
     {
         if (target == DNN_TARGET_OPENCL_FP16) applyTestTag(CV_TEST_TAG_DNN_SKIP_IE_OPENCL_FP16);
@@ -352,6 +352,7 @@ TEST_P(Test_TensorFlow_layers, concat_3d)
     if ((backend == DNN_BACKEND_INFERENCE_ENGINE_NGRAPH ||
          backend == DNN_BACKEND_INFERENCE_ENGINE_NN_BUILDER_2019) && target == DNN_TARGET_MYRIAD)
         applyTestTag(CV_TEST_TAG_DNN_SKIP_IE_MYRIAD, CV_TEST_TAG_DNN_SKIP_IE_NGRAPH, CV_TEST_TAG_DNN_SKIP_IE_NN_BUILDER);
+#endif
 
     runTensorFlowNet("concat_3d");
 }
@@ -429,13 +430,27 @@ TEST_P(Test_TensorFlow_layers, batch_norm3D)
 
 TEST_P(Test_TensorFlow_layers, slim_batch_norm)
 {
+#if defined(INF_ENGINE_RELEASE) && INF_ENGINE_VER_MAJOR_LT(2021040000)
     if (backend == DNN_BACKEND_INFERENCE_ENGINE_NN_BUILDER_2019)
         applyTestTag(CV_TEST_TAG_DNN_SKIP_IE_NN_BUILDER);
     if (backend == DNN_BACKEND_INFERENCE_ENGINE_NGRAPH)
         applyTestTag(CV_TEST_TAG_DNN_SKIP_IE_NGRAPH);
+#endif
     // Output values range: [-40.0597, 207.827]
-    double l1 = (target == DNN_TARGET_OPENCL_FP16 || target == DNN_TARGET_MYRIAD) ? 0.041 : default_l1;
-    double lInf = (target == DNN_TARGET_OPENCL_FP16 || target == DNN_TARGET_MYRIAD) ? 0.33 : default_lInf;
+    double l1 = default_l1;
+    double lInf = default_lInf;
+    if (target == DNN_TARGET_OPENCL_FP16 || target == DNN_TARGET_MYRIAD)
+    {
+        l1 = 0.041;
+        lInf = 0.33;
+    }
+#if defined(INF_ENGINE_RELEASE)
+    else if (backend == DNN_BACKEND_INFERENCE_ENGINE_NGRAPH && target == DNN_TARGET_CPU)
+    {
+        lInf = 0.0002;
+    }
+#endif
+
     runTensorFlowNet("slim_batch_norm", false, l1, lInf);
 }
 
@@ -562,7 +577,7 @@ TEST_P(Test_TensorFlow_layers, max_pool_grad)
 TEST_P(Test_TensorFlow_layers, ave_pool_same)
 {
     // Reference output values are in range [-0.519531, 0.112976]
-#if defined(INF_ENGINE_RELEASE) && INF_ENGINE_VER_MAJOR_GE(2019010000)
+#if defined(INF_ENGINE_RELEASE) && INF_ENGINE_VER_MAJOR_GE(2019010000) && INF_ENGINE_VER_MAJOR_LT(2021040000)
     if (target == DNN_TARGET_MYRIAD && getInferenceEngineVPUType() == CV_DNN_INFERENCE_ENGINE_VPU_TYPE_MYRIAD_X)
     {
         if (backend == DNN_BACKEND_INFERENCE_ENGINE_NN_BUILDER_2019)
@@ -576,29 +591,42 @@ TEST_P(Test_TensorFlow_layers, ave_pool_same)
 
 TEST_P(Test_TensorFlow_layers, MaxPooling3D)
 {
-#if defined(INF_ENGINE_RELEASE) && INF_ENGINE_VER_MAJOR_LT(2019010000)
-    applyTestTag(CV_TEST_TAG_DNN_SKIP_IE_VERSION);
+#if defined(INF_ENGINE_RELEASE) && INF_ENGINE_VER_MAJOR_EQ(2021040000)
+    if (backend == DNN_BACKEND_INFERENCE_ENGINE_NGRAPH)
+    {
+        // accuracy
+        if (target == DNN_TARGET_OPENCL || target == DNN_TARGET_OPENCL_FP16)
+            applyTestTag(target == DNN_TARGET_OPENCL ? CV_TEST_TAG_DNN_SKIP_IE_OPENCL : CV_TEST_TAG_DNN_SKIP_IE_OPENCL_FP16,
+                CV_TEST_TAG_DNN_SKIP_IE_NGRAPH, CV_TEST_TAG_DNN_SKIP_IE_VERSION
+            );
+        // IE exception: [ GENERAL_ERROR ]  AssertionFailed: !expired()
+        if (target == DNN_TARGET_MYRIAD)
+            applyTestTag(CV_TEST_TAG_DNN_SKIP_IE_MYRIAD, CV_TEST_TAG_DNN_SKIP_IE_NGRAPH, CV_TEST_TAG_DNN_SKIP_IE_VERSION);
+    }
 #endif
+#if defined(INF_ENGINE_RELEASE) && INF_ENGINE_VER_MAJOR_LT(2021040000)
     if (backend == DNN_BACKEND_INFERENCE_ENGINE_NN_BUILDER_2019 && target != DNN_TARGET_CPU)
         applyTestTag(CV_TEST_TAG_DNN_SKIP_IE_NN_BUILDER);  // Only CPU on DLIE backend is supported
     if (backend == DNN_BACKEND_INFERENCE_ENGINE_NGRAPH && target != DNN_TARGET_CPU)
         applyTestTag(CV_TEST_TAG_DNN_SKIP_IE_NGRAPH);  // Only CPU on DLIE backend is supported
-    if (target != DNN_TARGET_CPU)
-        throw SkipTestException("Only CPU is supported");
+#endif
+    if (backend == DNN_BACKEND_OPENCV && target != DNN_TARGET_CPU)
+        throw SkipTestException("Only CPU is supported");  // FIXIT use tags
+
     runTensorFlowNet("max_pool3d");
 }
 
 TEST_P(Test_TensorFlow_layers, AvePooling3D)
 {
-#if defined(INF_ENGINE_RELEASE) && INF_ENGINE_VER_MAJOR_LT(2019010000)
-    applyTestTag(CV_TEST_TAG_DNN_SKIP_IE_VERSION);
-#endif
+#if defined(INF_ENGINE_RELEASE) && INF_ENGINE_VER_MAJOR_LT(2021040000)
     if (backend == DNN_BACKEND_INFERENCE_ENGINE_NN_BUILDER_2019 && target != DNN_TARGET_CPU)
         applyTestTag(CV_TEST_TAG_DNN_SKIP_IE_NN_BUILDER);  // Only CPU on DLIE backend is supported
     if (backend == DNN_BACKEND_INFERENCE_ENGINE_NGRAPH && target != DNN_TARGET_CPU)
         applyTestTag(CV_TEST_TAG_DNN_SKIP_IE_NGRAPH);  // Only CPU on DLIE backend is supported
-    if (target != DNN_TARGET_CPU)
-        throw SkipTestException("Only CPU is supported");
+#endif
+    if (backend == DNN_BACKEND_OPENCV && target != DNN_TARGET_CPU)
+        throw SkipTestException("Only CPU is supported");  // FIXIT use tags
+
     runTensorFlowNet("ave_pool3d");
 }
 
@@ -628,10 +656,12 @@ TEST_P(Test_TensorFlow_layers, matmul)
 
 TEST_P(Test_TensorFlow_layers, reshape)
 {
+#if defined(INF_ENGINE_RELEASE) && INF_ENGINE_VER_MAJOR_LT(2021040000)
     if (backend == DNN_BACKEND_INFERENCE_ENGINE_NN_BUILDER_2019)
         applyTestTag(CV_TEST_TAG_DNN_SKIP_IE_NN_BUILDER);
     if (backend == DNN_BACKEND_INFERENCE_ENGINE_NGRAPH)
         applyTestTag(CV_TEST_TAG_DNN_SKIP_IE_NGRAPH);
+#endif
     runTensorFlowNet("shift_reshape_no_reorder");
     runTensorFlowNet("reshape_no_reorder");
     runTensorFlowNet("reshape_reduce");
@@ -1188,18 +1218,35 @@ TEST_P(Test_TensorFlow_layers, quantized)
 
 TEST_P(Test_TensorFlow_layers, lstm)
 {
+#if defined(INF_ENGINE_RELEASE) && INF_ENGINE_VER_MAJOR_LT(2021040000)
     if (backend == DNN_BACKEND_INFERENCE_ENGINE_NN_BUILDER_2019)
         applyTestTag(CV_TEST_TAG_DNN_SKIP_IE_NN_BUILDER);
     if (backend == DNN_BACKEND_INFERENCE_ENGINE_NGRAPH)
         applyTestTag(CV_TEST_TAG_DNN_SKIP_IE_NGRAPH);
+#endif
+#if defined(INF_ENGINE_RELEASE) && INF_ENGINE_VER_MAJOR_EQ(2021040000)
+    if (backend == DNN_BACKEND_INFERENCE_ENGINE_NGRAPH)
+    {
+        // Exception: Ngraph operation Reshape with name Reshape has dynamic output shape on 0 port, but CPU plug-in supports only static shape
+        if (target == DNN_TARGET_OPENCL || target == DNN_TARGET_OPENCL_FP16)
+            applyTestTag(target == DNN_TARGET_OPENCL ? CV_TEST_TAG_DNN_SKIP_IE_OPENCL : CV_TEST_TAG_DNN_SKIP_IE_OPENCL_FP16,
+                CV_TEST_TAG_DNN_SKIP_IE_NGRAPH, CV_TEST_TAG_DNN_SKIP_IE_VERSION
+            );
+        // Xlink
+        if (target == DNN_TARGET_MYRIAD)
+            applyTestTag(CV_TEST_TAG_DNN_SKIP_IE_MYRIAD, CV_TEST_TAG_DNN_SKIP_IE_NGRAPH, CV_TEST_TAG_DNN_SKIP_IE_VERSION);
+    }
+#endif
     if (backend == DNN_BACKEND_OPENCV && target == DNN_TARGET_OPENCL_FP16)
         applyTestTag(CV_TEST_TAG_DNN_SKIP_OPENCL_FP16);
+
     runTensorFlowNet("lstm", true);
     runTensorFlowNet("lstm", true, 0.0, 0.0, true);
 }
 
 TEST_P(Test_TensorFlow_layers, split)
 {
+
     if (backend == DNN_BACKEND_INFERENCE_ENGINE_NN_BUILDER_2019 && target == DNN_TARGET_MYRIAD)
         applyTestTag(CV_TEST_TAG_DNN_SKIP_IE_MYRIAD, CV_TEST_TAG_DNN_SKIP_IE_NN_BUILDER);
     if (backend == DNN_BACKEND_INFERENCE_ENGINE_NGRAPH)
@@ -1229,8 +1276,10 @@ TEST_P(Test_TensorFlow_layers, resize_nearest_neighbor_align_corners)
 
 TEST_P(Test_TensorFlow_layers, resize_nearest_neighbor_half_pixel)
 {
+#if defined(INF_ENGINE_RELEASE) && INF_ENGINE_VER_MAJOR_LT(2021040000)
     if (backend == DNN_BACKEND_INFERENCE_ENGINE_NGRAPH)
         applyTestTag(CV_TEST_TAG_DNN_SKIP_IE_NGRAPH);
+#endif
 
     runTensorFlowNet("resize_nearest_neighbor", false, 0.0, 0.0, false, "_half_pixel");
 }
@@ -1369,10 +1418,26 @@ TEST_P(Test_TensorFlow_layers, clip_by_value)
 
 TEST_P(Test_TensorFlow_layers, tf2_prelu)
 {
+#if defined(INF_ENGINE_RELEASE) && INF_ENGINE_VER_MAJOR_LT(2021040000)
     if (backend == DNN_BACKEND_INFERENCE_ENGINE_NN_BUILDER_2019)
         applyTestTag(CV_TEST_TAG_DNN_SKIP_IE_NN_BUILDER);
     if (backend == DNN_BACKEND_INFERENCE_ENGINE_NGRAPH)
         applyTestTag(CV_TEST_TAG_DNN_SKIP_IE_NGRAPH);
+#endif
+#if defined(INF_ENGINE_RELEASE) && INF_ENGINE_VER_MAJOR_EQ(2021040000)
+    if (backend == DNN_BACKEND_INFERENCE_ENGINE_NGRAPH)
+    {
+        // IE exception: Input prelu:StatefulPartitionedCall/StatefulPartitionedCall/sequential/p_re_lu/add hasn't been found in primitiveIDs map
+        if (target == DNN_TARGET_OPENCL || target == DNN_TARGET_OPENCL_FP16)
+            applyTestTag(target == DNN_TARGET_OPENCL ? CV_TEST_TAG_DNN_SKIP_IE_OPENCL : CV_TEST_TAG_DNN_SKIP_IE_OPENCL_FP16,
+                CV_TEST_TAG_DNN_SKIP_IE_NGRAPH, CV_TEST_TAG_DNN_SKIP_IE_VERSION
+            );
+        // IE exception: Eltwise node with name `StatefulPartitionedCall/StatefulPartitionedCall/sequential/p_re_lu/add` has invalid input/output dims configuration
+        if (target == DNN_TARGET_CPU)
+            applyTestTag(CV_TEST_TAG_DNN_SKIP_IE_CPU, CV_TEST_TAG_DNN_SKIP_IE_NGRAPH, CV_TEST_TAG_DNN_SKIP_IE_VERSION);
+    }
+#endif
+
     runTensorFlowNet("tf2_prelu");
 }
 
diff --git a/modules/dnn/test/test_torch_importer.cpp b/modules/dnn/test/test_torch_importer.cpp
index 96e8ac85a8..fdd5a4b923 100644
--- a/modules/dnn/test/test_torch_importer.cpp
+++ b/modules/dnn/test/test_torch_importer.cpp
@@ -211,23 +211,32 @@ TEST_P(Test_Torch_layers, net_lp_pooling_square)
 }
 TEST_P(Test_Torch_layers, net_lp_pooling_power)
 {
+#if defined(INF_ENGINE_RELEASE) && INF_ENGINE_VER_MAJOR_LT(2021040000)
     if (backend == DNN_BACKEND_INFERENCE_ENGINE_NGRAPH && target == DNN_TARGET_MYRIAD)
-        applyTestTag(CV_TEST_TAG_DNN_SKIP_IE_MYRIAD, CV_TEST_TAG_DNN_SKIP_IE_NGRAPH);
+        applyTestTag(CV_TEST_TAG_DNN_SKIP_IE_MYRIAD, CV_TEST_TAG_DNN_SKIP_IE_NGRAPH, CV_TEST_TAG_DNN_SKIP_IE_VERSION);
+#endif
     runTorchNet("net_lp_pooling_power", "", false, true);
 }
 
 TEST_P(Test_Torch_layers, net_conv_gemm_lrn)
 {
+#if defined(INF_ENGINE_RELEASE) && INF_ENGINE_VER_MAJOR_LT(2021040000)
     if (backend == DNN_BACKEND_INFERENCE_ENGINE_NN_BUILDER_2019 && target == DNN_TARGET_MYRIAD)
         applyTestTag(CV_TEST_TAG_DNN_SKIP_IE_MYRIAD, CV_TEST_TAG_DNN_SKIP_IE_NN_BUILDER);
     if (backend == DNN_BACKEND_INFERENCE_ENGINE_NGRAPH && target == DNN_TARGET_MYRIAD)
         applyTestTag(CV_TEST_TAG_DNN_SKIP_IE_MYRIAD, CV_TEST_TAG_DNN_SKIP_IE_NGRAPH);
+#endif
     double l1 = 0.0, lInf = 0.0;
     if (target == DNN_TARGET_OPENCL_FP16)
     {
         l1 = 0.046;
         lInf = 0.023;
     }
+    else if (target == DNN_TARGET_MYRIAD)
+    {
+        l1 = 0.02;
+        lInf = 0.05;
+    }
     // The OpenCL kernels use the native_ math functions which have
     // implementation defined accuracy, so we use relaxed thresholds. See
     // https://github.com/opencv/opencv/issues/9821 for more details.