diff --git a/include/onnxruntime/core/framework/tensor.h b/include/onnxruntime/core/framework/tensor.h
index ac98756964..46b6d830b3 100644
--- a/include/onnxruntime/core/framework/tensor.h
+++ b/include/onnxruntime/core/framework/tensor.h
@@ -72,9 +72,6 @@ class Tensor final {
   //Move is allowed
   ORT_DISALLOW_COPY_AND_ASSIGNMENT(Tensor);
 
-  ///requires other.buffer_deleter_ == nullptr
-  Tensor& ShallowCopy(const Tensor& other);
-
   Tensor(Tensor&& other);
 
   Tensor& operator=(Tensor&& other);
diff --git a/onnxruntime/core/framework/tensor.cc b/onnxruntime/core/framework/tensor.cc
index c78c7da9da..1dc3bf73fe 100644
--- a/onnxruntime/core/framework/tensor.cc
+++ b/onnxruntime/core/framework/tensor.cc
@@ -83,22 +83,6 @@ Tensor::~Tensor() {
   ReleaseBuffer();
 }
 
-Tensor& Tensor::ShallowCopy(const Tensor& other) {
-  // similar as above
-  ORT_ENFORCE(other.buffer_deleter_ == nullptr,
-              "Can't copy tensor with its owned buffer. Please transfer ownership by move.");
-
-  if (this != &other) {
-    dtype_ = other.dtype_;
-    alloc_info_ = other.alloc_info_;
-    shape_ = other.shape_;
-    byte_offset_ = other.byte_offset_;
-    p_data_ = other.p_data_;
-    buffer_deleter_ = nullptr;
-  }
-  return *this;
-}
-
 void Tensor::ReleaseBuffer() {
   if (buffer_deleter_) {
     // if current tensor is responsible for delete the buffer
diff --git a/onnxruntime/core/framework/utils.cc b/onnxruntime/core/framework/utils.cc
index fe996fdc1a..08b869c444 100644
--- a/onnxruntime/core/framework/utils.cc
+++ b/onnxruntime/core/framework/utils.cc
@@ -155,8 +155,11 @@ common::Status CopyOneInputAcrossDevices(const SessionState& session_state,
   // our CPU exec provider doesn't support copy from GPU->CPU
   if (required_provider_type != onnxruntime::kCpuExecutionProvider) {
     ORT_RETURN_IF_ERROR(required_provider->CopyTensor(input_tensor, *new_tensor));
-  } else {
+  } else if (input_provider_type != onnxruntime::kCpuExecutionProvider) {
     ORT_RETURN_IF_ERROR(p_input_provider->CopyTensor(input_tensor, *new_tensor));
+  } else {
+    //both tensors are on CPU.
+    return Status(common::ONNXRUNTIME, common::FAIL, "can't copy a tensor from CPU to CPU");
   }
 
   // } loop of node_info_vec
@@ -309,8 +312,11 @@ common::Status CopyOutputsAcrossDevices(const SessionState& session_state,
     // our CPU exec provider doesn't support copy from GPU->CPU
     if (fetched_provider_type != onnxruntime::kCpuExecutionProvider) {
       ORT_RETURN_IF_ERROR(p_fetched_provider->CopyTensor(fetched_tensor, *p_output_tensor));
-    } else {
+    } else if (output_provider_type != onnxruntime::kCpuExecutionProvider) {
       ORT_RETURN_IF_ERROR(p_output_provider->CopyTensor(fetched_tensor, *p_output_tensor));
+    } else {
+      //both tensors are on CPU.
+      return Status(common::ONNXRUNTIME, common::FAIL, "can't copy a tensor from CPU to CPU");
     }
   }
 
diff --git a/onnxruntime/core/providers/cpu/cpu_execution_provider.h b/onnxruntime/core/providers/cpu/cpu_execution_provider.h
index b8580a3d89..fa3e78c87c 100644
--- a/onnxruntime/core/providers/cpu/cpu_execution_provider.h
+++ b/onnxruntime/core/providers/cpu/cpu_execution_provider.h
@@ -50,18 +50,8 @@ class CPUExecutionProvider : public IExecutionProvider {
                 const std::vector<const KernelRegistry*>& kernel_registries) const override;
 
   ///requires src.buffer_deleter_ == nullptr
-  Status CopyTensor(const Tensor& src, Tensor& dst) const override {
-    ORT_ENFORCE(strcmp(dst.Location().name, CPU) == 0);
-
-    // Todo: support copy with different devices.
-    if (strcmp(src.Location().name, CPU) != 0) {
-      ORT_NOT_IMPLEMENTED("copy from ", src.Location().name, " is not implemented");
-    }
-
-    // no really copy needed if is copy to cpu.
-    dst.ShallowCopy(src);
-
-    return Status::OK();
+  Status CopyTensor(const Tensor&, Tensor&) const override {
+    return Status(common::ONNXRUNTIME, common::FAIL, "Shouldn't reach here. CPUExecutionProvider doesn't support CopyTensor");
   }
 
   const void* GetExecutionHandle() const noexcept override {