diff --git a/mlir/lib/IR/StandardTypes.cpp b/mlir/lib/IR/StandardTypes.cpp
--- a/mlir/lib/IR/StandardTypes.cpp
+++ b/mlir/lib/IR/StandardTypes.cpp
@@ -334,7 +334,7 @@
 
   // Check that memref is formed from allowed types.
   if (!elementType.isIntOrFloat() && !elementType.isa<VectorType>() &&
-      !elementType.isa<ComplexType>())
+      !elementType.isa<ComplexType>() && !elementType.isa<BaseMemRefType>())
     return emitOptionalError(location, "invalid memref element type"),
            MemRefType();
 
@@ -413,7 +413,7 @@
     unsigned memorySpace) {
   // Check that memref is formed from allowed types.
   if (!elementType.isIntOrFloat() && !elementType.isa<VectorType>() &&
-      !elementType.isa<ComplexType>())
+      !elementType.isa<ComplexType>() && !elementType.isa<BaseMemRefType>())
     return emitOptionalError(*loc, "invalid memref element type");
   return success();
 }
diff --git a/mlir/test/IR/parser.mlir b/mlir/test/IR/parser.mlir
--- a/mlir/test/IR/parser.mlir
+++ b/mlir/test/IR/parser.mlir
@@ -143,6 +143,15 @@
 // CHECK: func @unranked_memref_with_complex_elems(memref<*xcomplex<f32>>)
 func @unranked_memref_with_complex_elems(memref<*xcomplex<f32>>)
 
+// CHECK: func @memref_with_memref_elems(memref<1x?xmemref<f32>>)
+func @memref_with_memref_elems(memref<1x?xmemref<f32>>)
+
+// CHECK: func @unranked_memref_with_memref_elems(memref<*xmemref<f32>>)
+func @unranked_memref_with_memref_elems(memref<*xmemref<f32>>)
+
+// CHECK: func @functions_with_memref((memref<1x?x4x?x?xmemref<i32>, #map0>, memref<8xi8>) -> (), () -> ())
+func @functions_with_memref((memref<1x?x4x?x?xmemref<i32>, #map0, 0>, memref<8xi8, #map1, 0>) -> (), ()->())
+
 // CHECK: func @functions((memref<1x?x4x?x?xi32, #map0>, memref<8xi8>) -> (), () -> ())
 func @functions((memref<1x?x4x?x?xi32, #map0, 0>, memref<8xi8, #map1, 0>) -> (), ()->())