diff --git a/Lib/test/test_venv.py b/Lib/test/test_venv.py
index 1084a99a5e3..e13cd8cf989 100644
--- a/Lib/test/test_venv.py
+++ b/Lib/test/test_venv.py
@@ -9,6 +9,7 @@ import ensurepip
 import os
 import os.path
 import shutil
+import struct
 import subprocess
 import sys
 import tempfile
@@ -87,6 +88,14 @@ class BasicTest(BaseTest):
         self.isdir(self.bindir)
         self.isdir(self.include)
         self.isdir(*self.lib)
+        # Issue 21197
+        p = self.get_env_file('lib64')
+        conditions = ((struct.calcsize('P') == 8) and (os.name == 'posix') and
+                      (sys.platform != 'darwin'))
+        if conditions:
+            self.assertTrue(os.path.islink(p))
+        else:
+            self.assertFalse(os.path.exists(p))
         data = self.get_text_file_contents('pyvenv.cfg')
         if sys.platform == 'darwin' and ('__PYVENV_LAUNCHER__'
                                          in os.environ):
diff --git a/Lib/venv/__init__.py b/Lib/venv/__init__.py
index bbdd9113387..20dafc0353f 100644
--- a/Lib/venv/__init__.py
+++ b/Lib/venv/__init__.py
@@ -1,7 +1,7 @@
 """
 Virtual environment (venv) package for Python. Based on PEP 405.
 
-Copyright (C) 2011-2012 Vinay Sajip.
+Copyright (C) 2011-2014 Vinay Sajip.
 Licensed to the PSF under a contributor agreement.
 
 usage: python -m venv [-h] [--system-site-packages] [--symlinks] [--clear]
@@ -30,6 +30,7 @@ optional arguments:
 import logging
 import os
 import shutil
+import struct
 import subprocess
 import sys
 import types
@@ -132,10 +133,18 @@ class EnvBuilder:
         else:
             binname = 'bin'
             incpath = 'include'
-            libpath = os.path.join(env_dir, 'lib', 'python%d.%d' % sys.version_info[:2], 'site-packages')
+            libpath = os.path.join(env_dir, 'lib',
+                                   'python%d.%d' % sys.version_info[:2],
+                                   'site-packages')
         context.inc_path = path = os.path.join(env_dir, incpath)
         create_if_needed(path)
         create_if_needed(libpath)
+        # Issue 21197: create lib64 as a symlink to lib on 64-bit non-OS X POSIX
+        if ((struct.calcsize('P') == 8) and (os.name == 'posix') and
+            (sys.platform != 'darwin')):
+            p = os.path.join(env_dir, 'lib')
+            link_path = os.path.join(env_dir, 'lib64')
+            os.symlink(p, link_path)
         context.bin_path = binpath = os.path.join(env_dir, binname)
         context.bin_name = binname
         context.env_exe = os.path.join(binpath, exename)
diff --git a/Misc/NEWS b/Misc/NEWS
index a158999f982..26377fe23d1 100644
--- a/Misc/NEWS
+++ b/Misc/NEWS
@@ -41,6 +41,8 @@ Core and Builtins
 Library
 -------
 
+- Issue #21197: Add lib64 -> lib symlink in venvs on 64-bit non-OS X POSIX.
+
 - Issue #17498: Some SMTP servers disconnect after certain errors, violating
   strict RFC conformance.  Instead of losing the error code when we issue the
   subsequent RSET, smtplib now returns the error code and defers raising the