diff --git a/mlir/lib/Dialect/Linalg/IR/LinalgOps.cpp b/mlir/lib/Dialect/Linalg/IR/LinalgOps.cpp
--- a/mlir/lib/Dialect/Linalg/IR/LinalgOps.cpp
+++ b/mlir/lib/Dialect/Linalg/IR/LinalgOps.cpp
@@ -2595,6 +2595,15 @@
 
   LogicalResult matchAndRewrite(Operation *op,
                                 PatternRewriter &rewriter) const override {
+    if (auto copyOp = dyn_cast<CopyOp>(op)) {
+      assert(copyOp.hasBufferSemantics());
+      if (copyOp.input() == copyOp.output() &&
+          copyOp.inputPermutation() == copyOp.outputPermutation()) {
+        rewriter.eraseOp(op);
+        return success();
+      }
+    }
+
     if (!isa<GenericOp, IndexedGenericOp>(op))
       return failure();
     LinalgOp genericOp = cast<LinalgOp>(op);
diff --git a/mlir/test/Dialect/Linalg/canonicalize.mlir b/mlir/test/Dialect/Linalg/canonicalize.mlir
--- a/mlir/test/Dialect/Linalg/canonicalize.mlir
+++ b/mlir/test/Dialect/Linalg/canonicalize.mlir
@@ -789,3 +789,15 @@
 //       CHECK:   %[[INSERTED:.+]] = subtensor_insert %{{.+}} into %[[FILL]]
 //       CHECK:   %[[RESULT:.+]] = tensor.cast %[[INSERTED]]
 //       CHECK:   return %[[RESULT]]
+
+// -----
+
+// CHECK-LABEL: @self_copy
+func @self_copy(%arg0 : memref<2x3x?x4xf32>) {
+
+//   CHECK-NOT: linalg.copy
+  linalg.copy(%arg0, %arg0): memref<2x3x?x4xf32>, memref<2x3x?x4xf32>
+
+//   CHECK: return
+  return
+}