diff --git a/modules/dnn/src/onnx/onnx_importer.cpp b/modules/dnn/src/onnx/onnx_importer.cpp
index 41ff6c9b1e..6583d6cf62 100644
--- a/modules/dnn/src/onnx/onnx_importer.cpp
+++ b/modules/dnn/src/onnx/onnx_importer.cpp
@@ -475,7 +475,8 @@ void ONNXImporter::populateNet()
         for (int j = 0; j < inpShape.size(); ++j)
         {
             inpShape[j] = tensorShape.dim(j).dim_value();
-            if (!tensorShape.dim(j).dim_param().empty())
+            // NHW, NCHW(NHWC), NCDHW(NDHWC); do not set this flag if only N is dynamic
+            if (!tensorShape.dim(j).dim_param().empty() && !(j == 0 && inpShape.size() >= 3))
                 hasDynamicShapes = true;
         }
         if (!inpShape.empty() && !hasDynamicShapes)
@@ -1407,6 +1408,16 @@ void ONNXImporter::parseMul(LayerParams& layerParams, const opencv_onnx::NodePro
             //Replace input to Power
             node_proto.set_input(1, powerParams.name);
         }
+
+        const MatShape& broadShape = outShapes[node_proto.input(1)];
+        const size_t outShapeSize = outShapes[node_proto.input(0)].size();
+        const size_t diff = outShapeSize - broadShape.size();
+
+        size_t axis;
+        for (axis = diff; axis < broadShape.size() && broadShape[axis - diff] == 1; ++axis) {}
+
+        CV_Assert(axis != outShapeSize);
+        layerParams.set("axis", static_cast<int>(axis));
         layerParams.type = "Scale";
     }
     addLayer(layerParams, node_proto);
diff --git a/modules/dnn/test/test_onnx_importer.cpp b/modules/dnn/test/test_onnx_importer.cpp
index 07a0290b9b..bd96729be1 100644
--- a/modules/dnn/test/test_onnx_importer.cpp
+++ b/modules/dnn/test/test_onnx_importer.cpp
@@ -284,6 +284,7 @@ TEST_P(Test_ONNX_layers, Scale)
     if (backend == DNN_BACKEND_INFERENCE_ENGINE_NN_BUILDER_2019)
         applyTestTag(CV_TEST_TAG_DNN_SKIP_IE_NN_BUILDER);
     testONNXModels("scale");
+    testONNXModels("scale_broadcast", npy, 0, 0, false, true, 3);
 }
 
 TEST_P(Test_ONNX_layers, ReduceMean3D)
@@ -831,6 +832,7 @@ TEST_P(Test_ONNX_layers, DynamicAxes)
     testONNXModels("resize_opset11_torch1.6_dynamic_axes");
     testONNXModels("average_pooling_dynamic_axes");
     testONNXModels("maxpooling_sigmoid_dynamic_axes");
+    testONNXModels("dynamic_batch");
 }
 
 TEST_P(Test_ONNX_layers, MaxPool1d)