diff --git a/Doc/library/shutil.rst b/Doc/library/shutil.rst
index acba66258fe8f0..82a5abd657a4d6 100644
--- a/Doc/library/shutil.rst
+++ b/Doc/library/shutil.rst
@@ -54,6 +54,9 @@ Directory and files operations
    *dst* and return *dst* in the most efficient way possible.
    *src* and *dst* are path-like objects or path names given as strings.
 
+   When *src* is a named pipe or a Unix socket, :exc:`SpecialFileError`
+   is raised.
+
    *dst* must be the complete target file name; look at :func:`~shutil.copy`
    for a copy that accepts a target directory path.  If *src* and *dst*
    specify the same file, :exc:`SameFileError` is raised.
@@ -83,6 +86,11 @@ Directory and files operations
       copy the file more efficiently. See
       :ref:`shutil-platform-dependent-efficient-copy-operations` section.
 
+   .. versionchanged:: 3.12
+      Raise :exc:`~shutil.SpecialFileError` instead of :exc:`OSError` when
+      copying a Unix socket. Since the former is a subclass of the latter, this
+      change is backward compatible.
+
 .. exception:: SameFileError
 
    This exception is raised if source and destination in :func:`copyfile`
@@ -369,7 +377,7 @@ Directory and files operations
    If *copy_function* is given, it must be a callable that takes two arguments
    *src* and *dst*, and will be used to copy *src* to *dst* if
    :func:`os.rename` cannot be used.  If the source is a directory,
-   :func:`copytree` is called, passing it the :func:`copy_function`. The
+   :func:`copytree` is called, passing it the *copy_function*. The
    default *copy_function* is :func:`copy2`.  Using :func:`~shutil.copy` as the
    *copy_function* allows the move to succeed when it is not possible to also
    copy the metadata, at the expense of not copying any of the metadata.
diff --git a/Lib/shutil.py b/Lib/shutil.py
index b0576407e02ffb..e68068e5748248 100644
--- a/Lib/shutil.py
+++ b/Lib/shutil.py
@@ -242,10 +242,13 @@ def copyfile(src, dst, *, follow_symlinks=True):
             # File most likely does not exist
             pass
         else:
-            # XXX What about other special files? (sockets, devices...)
+            # XXX What about other special files? (devices...)
             if stat.S_ISFIFO(st.st_mode):
                 fn = fn.path if isinstance(fn, os.DirEntry) else fn
                 raise SpecialFileError("`%s` is a named pipe" % fn)
+            elif stat.S_ISSOCK(st.st_mode):
+                fn = fn.path if isinstance(fn, os.DirEntry) else fn
+                raise SpecialFileError("`%s` is a socket" % fn)
             if _WINDOWS and i == 0:
                 file_size = st.st_size
 
diff --git a/Lib/test/test_shutil.py b/Lib/test/test_shutil.py
index 1c0589ced9ea89..f9c5ccb1c82219 100644
--- a/Lib/test/test_shutil.py
+++ b/Lib/test/test_shutil.py
@@ -13,6 +13,7 @@
 import pathlib
 import subprocess
 import random
+import socket
 import string
 import contextlib
 import io
@@ -910,6 +911,28 @@ def test_copytree_named_pipe(self):
             shutil.rmtree(TESTFN, ignore_errors=True)
             shutil.rmtree(TESTFN2, ignore_errors=True)
 
+    @unittest.skipUnless(hasattr(socket, 'AF_UNIX'), 'requires socket.AF_UNIX')
+    def test_copytree_socket(self):
+        os.mkdir(TESTFN)
+        self.addCleanup(shutil.rmtree, TESTFN, ignore_errors=True)
+        self.addCleanup(shutil.rmtree, TESTFN2, ignore_errors=True)
+        sock_path = tempfile.mktemp(dir=TESTFN)
+
+        sock = socket.socket(socket.AF_UNIX, socket.SOCK_STREAM)
+        self.addCleanup(sock.close)
+        support.bind_unix_socket(sock, sock_path)
+        self.addCleanup(support.unlink, sock_path)
+
+        try:
+            shutil.copytree(TESTFN, TESTFN2)
+        except shutil.Error as e:
+            errors = e.args[0]
+            self.assertEqual(len(errors), 1)
+            src, dst, error_msg = errors[0]
+            self.assertEqual("`%s` is a socket" % sock_path, error_msg)
+        else:
+            self.fail("shutil.Error should have been raised")
+
     def test_copytree_special_func(self):
         src_dir = self.mkdtemp()
         dst_dir = os.path.join(self.mkdtemp(), 'destination')
@@ -1453,6 +1476,20 @@ def test_copyfile_named_pipe(self):
         finally:
             os.remove(TESTFN)
 
+    @unittest.skipUnless(hasattr(socket, 'AF_UNIX'), 'requires socket.AF_UNIX')
+    def test_copyfile_socket(self):
+        tmp_dir = self.mkdtemp()
+        src = tempfile.mktemp(dir=tmp_dir)
+        dst = os.path.join(tmp_dir, 'dst')
+
+        sock = socket.socket(socket.AF_UNIX, socket.SOCK_STREAM)
+        self.addCleanup(sock.close)
+        support.bind_unix_socket(sock, src)
+        self.addCleanup(support.unlink, src)
+
+        self.assertRaises(shutil.SpecialFileError,
+                            shutil.copyfile, src, dst)
+
     def test_copyfile_return_value(self):
         # copytree returns its destination path.
         src_dir = self.mkdtemp()
diff --git a/Misc/NEWS.d/next/Library/2019-10-03-17-26-27.bpo-37700.pec3ne.rst b/Misc/NEWS.d/next/Library/2019-10-03-17-26-27.bpo-37700.pec3ne.rst
new file mode 100644
index 00000000000000..dfdaa7ad574eea
--- /dev/null
+++ b/Misc/NEWS.d/next/Library/2019-10-03-17-26-27.bpo-37700.pec3ne.rst
@@ -0,0 +1,2 @@
+:func:`shutil.copyfile` always raises :exc:`shutil.SpecialFileError`
+when trying to copy a Unix socket.