diff --git a/Lib/SocketServer.py b/Lib/SocketServer.py
index 64a86d11c19..cf8a365fb8a 100644
--- a/Lib/SocketServer.py
+++ b/Lib/SocketServer.py
@@ -396,6 +396,8 @@ class StreamRequestHandler(BaseRequestHandler):
 
     def finish(self):
         self.wfile.flush()
+        self.wfile.close()
+        self.rfile.close()
 
 
 class DatagramRequestHandler(BaseRequestHandler):