diff --git a/Doc/library/tarfile.rst b/Doc/library/tarfile.rst
--- a/Doc/library/tarfile.rst
+++ b/Doc/library/tarfile.rst
@@ -367,7 +367,7 @@
    available.
 
 
-.. method:: TarFile.extractall(path=".", members=None)
+.. method:: TarFile.extractall(path=".", members=None, numeric_owner=False)
 
    Extract all members from the archive to the current working directory or
    directory *path*. If optional *members* is given, it must be a subset of the
@@ -377,6 +377,9 @@
    reset each time a file is created in it. And, if a directory's permissions do
    not allow writing, extracting files to it will fail.
 
+   If *numeric_owner* is :const:`True`, only the (uid, gid) numbers are used to
+   set the owner/group for the extracted files.
+
    .. warning::
 
       Never extract archives from untrusted sources without prior inspection.
@@ -385,13 +388,14 @@
       dots ``".."``.
 
 
-.. method:: TarFile.extract(member, path="", set_attrs=True)
+.. method:: TarFile.extract(member, path="", set_attrs=True, numeric_owner=False)
 
    Extract a member from the archive to the current working directory, using its
    full name. Its file information is extracted as accurately as possible. *member*
    may be a filename or a :class:`TarInfo` object. You can specify a different
    directory using *path*. File attributes (owner, mtime, mode) are set unless
-   *set_attrs* is false.
+   *set_attrs* is false. If *numeric_owner* is :const:`True`, only the (uid, gid)
+   numbers are used to set the owner/group for the extracted files.
 
    .. note::
 
@@ -827,4 +831,3 @@
 because all the metadata is stored using *UTF-8*. *encoding* is only used in
 the rare cases when binary pax headers are decoded or when strings with
 surrogate characters are stored.
-
diff --git a/Lib/tarfile.py b/Lib/tarfile.py
--- a/Lib/tarfile.py
+++ b/Lib/tarfile.py
@@ -1972,12 +1972,13 @@
 
         self.members.append(tarinfo)
 
-    def extractall(self, path=".", members=None):
+    def extractall(self, path=".", members=None, numeric_owner=False):
         """Extract all members from the archive to the current working
            directory and set owner, modification time and permissions on
            directories afterwards. `path' specifies a different directory
            to extract to. `members' is optional and must be a subset of the
-           list returned by getmembers().
+           list returned by getmembers(). If `numeric_owner` is True, only
+           the numbers for user/group names are used and not the names.
         """
         directories = []
 
@@ -1991,7 +1992,8 @@
                 tarinfo = copy.copy(tarinfo)
                 tarinfo.mode = 0o700
             # Do not set_attrs directories, as we will do that further down
-            self.extract(tarinfo, path, set_attrs=not tarinfo.isdir())
+            self.extract(tarinfo, path, set_attrs=not tarinfo.isdir(),
+                         numeric_owner=numeric_owner)
 
         # Reverse sort directories.
         directories.sort(key=lambda a: a.name)
@@ -2001,7 +2003,7 @@
         for tarinfo in directories:
             dirpath = os.path.join(path, tarinfo.name)
             try:
-                self.chown(tarinfo, dirpath)
+                self.chown(tarinfo, dirpath, numeric_owner=numeric_owner)
                 self.utime(tarinfo, dirpath)
                 self.chmod(tarinfo, dirpath)
             except ExtractError as e:
@@ -2010,12 +2012,14 @@
                 else:
                     self._dbg(1, "tarfile: %s" % e)
 
-    def extract(self, member, path="", set_attrs=True):
+    def extract(self, member, path="", set_attrs=True, numeric_owner=False):
         """Extract a member from the archive to the current working directory,
            using its full name. Its file information is extracted as accurately
            as possible. `member' may be a filename or a TarInfo object. You can
            specify a different directory using `path'. File attributes (owner,
-           mtime, mode) are set unless `set_attrs' is False.
+           mtime, mode) are set unless `set_attrs' is False. If `numeric_owner`
+           is True, only the numbers for user/group names are used and not
+           the names.
         """
         self._check("r")
 
@@ -2030,7 +2034,8 @@
 
         try:
             self._extract_member(tarinfo, os.path.join(path, tarinfo.name),
-                                 set_attrs=set_attrs)
+                                 set_attrs=set_attrs,
+                                 numeric_owner=numeric_owner)
         except OSError as e:
             if self.errorlevel > 0:
                 raise
@@ -2076,7 +2081,8 @@
             # blkdev, etc.), return None instead of a file object.
             return None
 
-    def _extract_member(self, tarinfo, targetpath, set_attrs=True):
+    def _extract_member(self, tarinfo, targetpath, set_attrs=True,
+                        numeric_owner=False):
         """Extract the TarInfo object tarinfo to a physical
            file called targetpath.
         """
@@ -2114,7 +2120,7 @@
             self.makefile(tarinfo, targetpath)
 
         if set_attrs:
-            self.chown(tarinfo, targetpath)
+            self.chown(tarinfo, targetpath, numeric_owner)
             if not tarinfo.issym():
                 self.chmod(tarinfo, targetpath)
                 self.utime(tarinfo, targetpath)
@@ -2203,19 +2209,24 @@
             except KeyError:
                 raise ExtractError("unable to resolve link inside archive")
 
-    def chown(self, tarinfo, targetpath):
-        """Set owner of targetpath according to tarinfo.
+    def chown(self, tarinfo, targetpath, numeric_owner=False):
+        """Set owner of targetpath according to tarinfo. If numeric_owner
+           is True, use .gid/.uid instead of .gname/.uname.
         """
         if pwd and hasattr(os, "geteuid") and os.geteuid() == 0:
             # We have to be root to do so.
-            try:
-                g = grp.getgrnam(tarinfo.gname)[2]
-            except KeyError:
+            if numeric_owner:
                 g = tarinfo.gid
-            try:
-                u = pwd.getpwnam(tarinfo.uname)[2]
-            except KeyError:
                 u = tarinfo.uid
+            else:
+                try:
+                    g = grp.getgrnam(tarinfo.gname)[2]
+                except KeyError:
+                    g = tarinfo.gid
+                try:
+                    u = pwd.getpwnam(tarinfo.uname)[2]
+                except KeyError:
+                    u = tarinfo.uid
             try:
                 if tarinfo.issym() and hasattr(os, "lchown"):
                     os.lchown(targetpath, u, g)
diff --git a/Lib/test/test_tarfile.py b/Lib/test/test_tarfile.py
--- a/Lib/test/test_tarfile.py
+++ b/Lib/test/test_tarfile.py
@@ -4,6 +4,7 @@
 from hashlib import md5
 
 import unittest
+import unittest.mock
 import tarfile
 
 from test import support, script_helper
@@ -2264,6 +2265,92 @@
         self._test_partial_input("r:bz2")
 
 
+def root_is_uid_gid_0():
+    try:
+        import pwd, grp
+    except ImportError:
+        return False
+    if pwd.getpwuid(0)[0] != "root":
+        return False
+    if grp.getgrgid(0)[0] != "root":
+        return False
+    return True
+
+
+@unittest.skipUnless(root_is_uid_gid_0(), "uid=0,gid=0 must be named 'root'")
+class NumericOwnerTest(unittest.TestCase):
+
+    def _make_test_archive(self, fname, dirname):
+        fobj = io.BytesIO(b"content")
+
+        # ceate a tar file with a file, a directory, and a file within that directory
+        with tarfile.open(tmpname, "w") as w:
+            t = tarfile.TarInfo(fname)
+            t.uid = 99
+            t.gid = 98
+            t.uname = 'root'
+            t.gname = 'root'
+            w.addfile(t, fobj)
+
+            t = tarfile.TarInfo(dirname + '/')
+            t.uid = 77
+            t.gid = 76
+            t.uname = 'root'
+            t.gname = 'root'
+            t.type = tarfile.DIRTYPE
+            w.addfile(t)
+
+            t = tarfile.TarInfo(dirname + '/' + fname)
+            t.uid = 88
+            t.gid = 87
+            t.uname = 'root'
+            t.gname = 'root'
+            w.addfile(t, fobj)
+        return tmpname
+
+    @unittest.mock.patch("os.chown")
+    @unittest.mock.patch("os.geteuid")
+    def test_extract_with_numeric_owner(self, mock_geteuid, mock_chown):
+        mock_geteuid.return_value = 0
+        fname = 'numeric-owner-testfile'
+        dirname = 'dir'
+        testtar = self._make_test_archive(fname, dirname)
+        with tarfile.open(testtar) as r:
+            r.extract(fname, TEMPDIR, numeric_owner=True)
+            r.extract(dirname + '/' + fname , TEMPDIR, numeric_owner=True)
+        mock_chown.assert_has_calls([unittest.mock.call(os.path.join(TEMPDIR, fname), 99, 98),
+                                     unittest.mock.call(os.path.join(TEMPDIR, dirname, fname), 88, 87),
+                                     ],
+                                    any_order=True)
+
+    @unittest.mock.patch("os.chown")
+    @unittest.mock.patch("os.geteuid")
+    def test_extractall_with_numeric_owner(self, mock_geteuid, mock_chown):
+        mock_geteuid.return_value = 0
+        fname = 'numeric-owner-testfile'
+        dirname = 'dir'
+        testtar = self._make_test_archive(fname, dirname)
+        with tarfile.open(testtar) as r:
+            r.extractall(TEMPDIR, numeric_owner=True)
+        targetpath = os.path.join(TEMPDIR, fname)
+        mock_chown.assert_has_calls([unittest.mock.call(os.path.join(TEMPDIR, fname), 99, 98),
+                                     unittest.mock.call(os.path.join(TEMPDIR, dirname), 77, 76),
+                                     unittest.mock.call(os.path.join(TEMPDIR, dirname, fname), 88, 87),
+                                     ],
+                                    any_order=True)
+
+    @unittest.mock.patch("os.chown")
+    @unittest.mock.patch("os.geteuid")
+    def test_extract_without_numeric_owner(self, mock_geteuid, mock_chown):
+        mock_geteuid.return_value = 0
+        fname = 'numeric-owner-testfile'
+        dirname = 'dir'
+        testtar = self._make_test_archive(fname, dirname)
+        with tarfile.open(testtar) as r:
+            r.extract(fname, TEMPDIR, numeric_owner=False)
+        mock_chown.assert_called_with(os.path.join(TEMPDIR, fname), 0, 0)
+
+
 def setUpModule():
     support.unlink(TEMPDIR)
     os.makedirs(TEMPDIR)
diff --git a/Misc/ACKS b/Misc/ACKS
--- a/Misc/ACKS
+++ b/Misc/ACKS
@@ -1451,6 +1451,7 @@
 Pauli Virtanen
 Frank Visser
 Johannes Vogel
+Michael Vogt
 Radu Voicilas
 Alex Volkov
 Martijn Vries