diff --git a/Doc/library/pathlib.rst b/Doc/library/pathlib.rst
index 5a819175cf1..34ab3b8edf9 100644
--- a/Doc/library/pathlib.rst
+++ b/Doc/library/pathlib.rst
@@ -919,7 +919,7 @@ call fails (for example because the path doesn't exist):
    to an existing file or directory, it will be unconditionally replaced.
 
 
-.. method:: Path.resolve()
+.. method:: Path.resolve(strict=False)
 
    Make the path absolute, resolving any symlinks.  A new path object is
    returned::
@@ -936,10 +936,14 @@ call fails (for example because the path doesn't exist):
       >>> p.resolve()
       PosixPath('/home/antoine/pathlib/setup.py')
 
-   If the path doesn't exist, :exc:`FileNotFoundError` is raised.  If an
-   infinite loop is encountered along the resolution path,
-   :exc:`RuntimeError` is raised.
+   If the path doesn't exist and *strict* is ``True``, :exc:`FileNotFoundError`
+   is raised.  If *strict* is ``False``, the path is resolved as far as possible
+   and any remainder is appended without checking whether it exists.  If an
+   infinite loop is encountered along the resolution path, :exc:`RuntimeError`
+   is raised.
 
+   .. versionadded:: 3.6
+      The *strict* argument.
 
 .. method:: Path.rglob(pattern)
 
diff --git a/Lib/pathlib.py b/Lib/pathlib.py
index 1b5ab387a62..69653938ef7 100644
--- a/Lib/pathlib.py
+++ b/Lib/pathlib.py
@@ -178,12 +178,26 @@ class _WindowsFlavour(_Flavour):
     def casefold_parts(self, parts):
         return [p.lower() for p in parts]
 
-    def resolve(self, path):
+    def resolve(self, path, strict=False):
         s = str(path)
         if not s:
             return os.getcwd()
+        previous_s = None
         if _getfinalpathname is not None:
-            return self._ext_to_normal(_getfinalpathname(s))
+            if strict:
+                return self._ext_to_normal(_getfinalpathname(s))
+            else:
+                while True:
+                    try:
+                        s = self._ext_to_normal(_getfinalpathname(s))
+                    except FileNotFoundError:
+                        previous_s = s
+                        s = os.path.abspath(os.path.join(s, os.pardir))
+                    else:
+                        if previous_s is None:
+                            return s
+                        else:
+                            return s + os.path.sep + os.path.basename(previous_s)
         # Means fallback on absolute
         return None
 
@@ -285,7 +299,7 @@ class _PosixFlavour(_Flavour):
     def casefold_parts(self, parts):
         return parts
 
-    def resolve(self, path):
+    def resolve(self, path, strict=False):
         sep = self.sep
         accessor = path._accessor
         seen = {}
@@ -315,7 +329,10 @@ class _PosixFlavour(_Flavour):
                     target = accessor.readlink(newpath)
                 except OSError as e:
                     if e.errno != EINVAL:
-                        raise
+                        if strict:
+                            raise
+                        else:
+                            return newpath
                     # Not a symlink
                     path = newpath
                 else:
@@ -1092,7 +1109,7 @@ class Path(PurePath):
         obj._init(template=self)
         return obj
 
-    def resolve(self):
+    def resolve(self, strict=False):
         """
         Make the path absolute, resolving all symlinks on the way and also
         normalizing it (for example turning slashes into backslashes under
@@ -1100,7 +1117,7 @@ class Path(PurePath):
         """
         if self._closed:
             self._raise_closed()
-        s = self._flavour.resolve(self)
+        s = self._flavour.resolve(self, strict=strict)
         if s is None:
             # No symlink resolution => for consistency, raise an error if
             # the path doesn't exist or is forbidden
diff --git a/Lib/test/test_pathlib.py b/Lib/test/test_pathlib.py
index 2f2ba3cbfc7..f98c1febb5c 100644
--- a/Lib/test/test_pathlib.py
+++ b/Lib/test/test_pathlib.py
@@ -1486,8 +1486,8 @@ class _BasePathTest(object):
         self.assertEqual(set(p.glob("../xyzzy")), set())
 
 
-    def _check_resolve(self, p, expected):
-        q = p.resolve()
+    def _check_resolve(self, p, expected, strict=True):
+        q = p.resolve(strict)
         self.assertEqual(q, expected)
 
     # this can be used to check both relative and absolute resolutions
@@ -1498,8 +1498,17 @@ class _BasePathTest(object):
         P = self.cls
         p = P(BASE, 'foo')
         with self.assertRaises(OSError) as cm:
-            p.resolve()
+            p.resolve(strict=True)
         self.assertEqual(cm.exception.errno, errno.ENOENT)
+        # Non-strict
+        self.assertEqual(str(p.resolve(strict=False)),
+                         os.path.join(BASE, 'foo'))
+        p = P(BASE, 'foo', 'in', 'spam')
+        self.assertEqual(str(p.resolve(strict=False)),
+                         os.path.join(BASE, 'foo'))
+        p = P(BASE, '..', 'foo', 'in', 'spam')
+        self.assertEqual(str(p.resolve(strict=False)),
+                         os.path.abspath(os.path.join('foo')))
         # These are all relative symlinks
         p = P(BASE, 'dirB', 'fileB')
         self._check_resolve_relative(p, p)
@@ -1509,6 +1518,18 @@ class _BasePathTest(object):
         self._check_resolve_relative(p, P(BASE, 'dirB', 'fileB'))
         p = P(BASE, 'dirB', 'linkD', 'fileB')
         self._check_resolve_relative(p, P(BASE, 'dirB', 'fileB'))
+        # Non-strict
+        p = P(BASE, 'dirA', 'linkC', 'fileB', 'foo', 'in', 'spam')
+        self._check_resolve_relative(p, P(BASE, 'dirB', 'fileB', 'foo'), False)
+        p = P(BASE, 'dirA', 'linkC', '..', 'foo', 'in', 'spam')
+        if os.name == 'nt':
+            # In Windows, if linkY points to dirB, 'dirA\linkY\..'
+            # resolves to 'dirA' without resolving linkY first.
+            self._check_resolve_relative(p, P(BASE, 'dirA', 'foo'), False)
+        else:
+            # In Posix, if linkY points to dirB, 'dirA/linkY/..'
+            # resolves to 'dirB/..' first before resolving to parent of dirB.
+            self._check_resolve_relative(p, P(BASE, 'foo'), False)
         # Now create absolute symlinks
         d = tempfile.mkdtemp(suffix='-dirD')
         self.addCleanup(support.rmtree, d)
@@ -1516,6 +1537,18 @@ class _BasePathTest(object):
         os.symlink(join('dirB'), os.path.join(d, 'linkY'))
         p = P(BASE, 'dirA', 'linkX', 'linkY', 'fileB')
         self._check_resolve_absolute(p, P(BASE, 'dirB', 'fileB'))
+        # Non-strict
+        p = P(BASE, 'dirA', 'linkX', 'linkY', 'foo', 'in', 'spam')
+        self._check_resolve_relative(p, P(BASE, 'dirB', 'foo'), False)
+        p = P(BASE, 'dirA', 'linkX', 'linkY', '..', 'foo', 'in', 'spam')
+        if os.name == 'nt':
+            # In Windows, if linkY points to dirB, 'dirA\linkY\..'
+            # resolves to 'dirA' without resolving linkY first.
+            self._check_resolve_relative(p, P(d, 'foo'), False)
+        else:
+            # In Posix, if linkY points to dirB, 'dirA/linkY/..'
+            # resolves to 'dirB/..' first before resolving to parent of dirB.
+            self._check_resolve_relative(p, P(BASE, 'foo'), False)
 
     @with_symlinks
     def test_resolve_dot(self):
@@ -1525,7 +1558,11 @@ class _BasePathTest(object):
         self.dirlink(os.path.join('0', '0'), join('1'))
         self.dirlink(os.path.join('1', '1'), join('2'))
         q = p / '2'
-        self.assertEqual(q.resolve(), p)
+        self.assertEqual(q.resolve(strict=True), p)
+        r = q / '3' / '4'
+        self.assertRaises(FileNotFoundError, r.resolve, strict=True)
+        # Non-strict
+        self.assertEqual(r.resolve(strict=False), p / '3')
 
     def test_with(self):
         p = self.cls(BASE)
@@ -1972,10 +2009,10 @@ class PathTest(_BasePathTest, unittest.TestCase):
 class PosixPathTest(_BasePathTest, unittest.TestCase):
     cls = pathlib.PosixPath
 
-    def _check_symlink_loop(self, *args):
+    def _check_symlink_loop(self, *args, strict=True):
         path = self.cls(*args)
         with self.assertRaises(RuntimeError):
-            print(path.resolve())
+            print(path.resolve(strict))
 
     def test_open_mode(self):
         old_mask = os.umask(0)
@@ -2008,7 +2045,6 @@ class PosixPathTest(_BasePathTest, unittest.TestCase):
 
     @with_symlinks
     def test_resolve_loop(self):
-        # Loop detection for broken symlinks under POSIX
         # Loops with relative symlinks
         os.symlink('linkX/inside', join('linkX'))
         self._check_symlink_loop(BASE, 'linkX')
@@ -2016,6 +2052,8 @@ class PosixPathTest(_BasePathTest, unittest.TestCase):
         self._check_symlink_loop(BASE, 'linkY')
         os.symlink('linkZ/../linkZ', join('linkZ'))
         self._check_symlink_loop(BASE, 'linkZ')
+        # Non-strict
+        self._check_symlink_loop(BASE, 'linkZ', 'foo', strict=False)
         # Loops with absolute symlinks
         os.symlink(join('linkU/inside'), join('linkU'))
         self._check_symlink_loop(BASE, 'linkU')
@@ -2023,6 +2061,8 @@ class PosixPathTest(_BasePathTest, unittest.TestCase):
         self._check_symlink_loop(BASE, 'linkV')
         os.symlink(join('linkW/../linkW'), join('linkW'))
         self._check_symlink_loop(BASE, 'linkW')
+        # Non-strict
+        self._check_symlink_loop(BASE, 'linkW', 'foo', strict=False)
 
     def test_glob(self):
         P = self.cls
diff --git a/Misc/NEWS b/Misc/NEWS
index 3c280c545f3..31c3703b546 100644
--- a/Misc/NEWS
+++ b/Misc/NEWS
@@ -114,6 +114,9 @@ Core and Builtins
 Library
 -------
 
+- Issue #19717: Makes Path.resolve() succeed on paths that do not exist.
+  Patch by Vajrasky Kok
+
 - Issue #28563: Fixed possible DoS and arbitrary code execution when handle
   plural form selections in the gettext module.  The expression parser now
   supports exact syntax supported by GNU gettext.