diff --git a/mlir/lib/Dialect/MemRef/IR/MemRefOps.cpp b/mlir/lib/Dialect/MemRef/IR/MemRefOps.cpp
--- a/mlir/lib/Dialect/MemRef/IR/MemRefOps.cpp
+++ b/mlir/lib/Dialect/MemRef/IR/MemRefOps.cpp
@@ -486,11 +486,25 @@
     return success(modified);
   }
 };
+
+/// Fold memref.copy(%x, %x).
+struct FoldSelfCopy : public OpRewritePattern<CopyOp> {
+  using OpRewritePattern<CopyOp>::OpRewritePattern;
+
+  LogicalResult matchAndRewrite(CopyOp copyOp,
+                                PatternRewriter &rewriter) const override {
+    if (copyOp.source() != copyOp.target())
+      return failure();
+
+    rewriter.eraseOp(copyOp);
+    return success();
+  }
+};
 } // namespace
 
 void CopyOp::getCanonicalizationPatterns(RewritePatternSet &results,
                                          MLIRContext *context) {
-  results.add<FoldCopyOfCast>(context);
+  results.add<FoldCopyOfCast, FoldSelfCopy>(context);
 }
 
 //===----------------------------------------------------------------------===//
diff --git a/mlir/test/Dialect/MemRef/canonicalize.mlir b/mlir/test/Dialect/MemRef/canonicalize.mlir
--- a/mlir/test/Dialect/MemRef/canonicalize.mlir
+++ b/mlir/test/Dialect/MemRef/canonicalize.mlir
@@ -525,3 +525,13 @@
 //  CHECK-SAME:     %[[m1:.*]]: memref<?xf32>, %[[m2:.*]]: memref<*xf32>
 //       CHECK:   %[[casted2:.*]] = memref.cast %[[m2]]
 //       CHECK:   memref.copy %[[m1]], %[[casted2]]
+
+// -----
+
+func @self_copy(%m1: memref<?xf32>) {
+  memref.copy %m1, %m1 : memref<?xf32> to memref<?xf32>
+  return
+}
+
+// CHECK-LABEL: func @self_copy
+//  CHECK-NEXT:   return