diff --git a/Lib/subprocess.py b/Lib/subprocess.py
--- a/Lib/subprocess.py
+++ b/Lib/subprocess.py
@@ -348,6 +348,7 @@
 import signal
 import builtins
 import warnings
+import errno
 
 # Exception classes used by this module.
 class SubprocessError(Exception): pass
@@ -396,7 +397,6 @@
 else:
     import select
     _has_poll = hasattr(select, 'poll')
-    import errno
     import fcntl
     import pickle
 
@@ -831,7 +831,11 @@
             stderr = None
             if self.stdin:
                 if input:
-                    self.stdin.write(input)
+                    try:
+                        self.stdin.write(input)
+                    except IOError as e:
+                        if e.errno != errno.EPIPE and e.errno != errno.EINVAL:
+                            raise
                 self.stdin.close()
             elif self.stdout:
                 stdout = self.stdout.read()
@@ -1105,7 +1109,11 @@
 
             if self.stdin:
                 if input is not None:
-                    self.stdin.write(input)
+                    try:
+                        self.stdin.write(input)
+                    except IOError as e:
+                        if e.errno != errno.EPIPE:
+                            raise
                 self.stdin.close()
 
             # Wait for the reader threads, or time out.  If we time out, the
@@ -1619,9 +1627,16 @@
                     if mode & select.POLLOUT:
                         chunk = self._input[self._input_offset :
                                             self._input_offset + _PIPE_BUF]
-                        self._input_offset += os.write(fd, chunk)
-                        if self._input_offset >= len(self._input):
-                            close_unregister_and_remove(fd)
+                        try:
+                            self._input_offset += os.write(fd, chunk)
+                        except OSError as e:
+                            if e.errno == errno.EPIPE:
+                                close_unregister_and_remove(fd)
+                            else:
+                                raise
+                        else:
+                            if self._input_offset >= len(self._input):
+                                close_unregister_and_remove(fd)
                     elif mode & select_POLLIN_POLLPRI:
                         data = os.read(fd, 4096)
                         if not data:
@@ -1686,11 +1701,19 @@
                 if self.stdin in wlist:
                     chunk = self._input[self._input_offset :
                                         self._input_offset + _PIPE_BUF]
-                    bytes_written = os.write(self.stdin.fileno(), chunk)
-                    self._input_offset += bytes_written
-                    if self._input_offset >= len(self._input):
-                        self.stdin.close()
-                        self._write_set.remove(self.stdin)
+                    try:
+                        bytes_written = os.write(self.stdin.fileno(), chunk)
+                    except OSError as e:
+                        if e.errno == errno.EPIPE:
+                            self.stdin.close()
+                            self._write_set.remove(self.stdin)
+                        else:
+                            raise
+                    else:
+                        self._input_offset += bytes_written
+                        if self._input_offset >= len(self._input):
+                            self.stdin.close()
+                            self._write_set.remove(self.stdin)
 
                 if self.stdout in rlist:
                     data = os.read(self.stdout.fileno(), 1024)
diff --git a/Lib/test/test_subprocess.py b/Lib/test/test_subprocess.py
--- a/Lib/test/test_subprocess.py
+++ b/Lib/test/test_subprocess.py
@@ -720,6 +720,24 @@
         self.assertFalse(os.path.exists(ofname))
         self.assertFalse(os.path.exists(efname))
 
+    def test_communicate_epipe(self):
+        # Issue 10963: communicate() should hide EPIPE
+        p = subprocess.Popen([sys.executable, "-c", 'pass'],
+                             stdin=subprocess.PIPE,
+                             stdout=subprocess.PIPE,
+                             stderr=subprocess.PIPE)
+        self.addCleanup(p.stdout.close)
+        self.addCleanup(p.stderr.close)
+        self.addCleanup(p.stdin.close)
+        p.communicate(b"x" * 2**20)
+
+    def test_communicate_epipe_only_stdin(self):
+        # Issue 10963: communicate() should hide EPIPE
+        p = subprocess.Popen([sys.executable, "-c", 'pass'],
+                             stdin=subprocess.PIPE)
+        self.addCleanup(p.stdin.close)
+        time.sleep(2)
+        p.communicate(b"x" * 2**20)
 
 # context manager
 class _SuppressCoreFiles(object):