diff --git a/Doc/library/crypt.rst b/Doc/library/crypt.rst
index d25c626a175854a..50d949244f64253 100644
--- a/Doc/library/crypt.rst
+++ b/Doc/library/crypt.rst
@@ -43,7 +43,8 @@ are available on all platforms):
 .. data:: METHOD_SHA512
 
    A Modular Crypt Format method with 16 character salt and 86 character
-   hash based on the SHA-512 hash function.  This is the strongest method.
+   hash based on the SHA-512 hash function.  This is the strongest method
+   supported on all UNIX-based operating systems.
 
 .. data:: METHOD_SHA256
 
@@ -67,6 +68,14 @@ are available on all platforms):
    The traditional method with a 2 character salt and 13 characters of
    hash.  This is the weakest method.
 
+   .. versionadded:: 3.10
+
+.. data:: METHOD_YESCRYPT
+
+   Another Modular Crypt Format method with 24 character salt and 43
+   character hash based on the yescrypt hash function.  This is the
+   strongest method supported on Linux distributions using libxcrypt.
+
 
 Module Attributes
 -----------------
diff --git a/Lib/crypt.py b/Lib/crypt.py
index 33dbc46bb3e96be..98aa43c5ce32068 100644
--- a/Lib/crypt.py
+++ b/Lib/crypt.py
@@ -45,7 +45,14 @@ def mksalt(method=None, *, rounds=None):
     else:  # modular
         s = f'${method.ident}$'
 
-    if method.ident and method.ident[0] == '2':  # Blowfish variants
+    if method.ident and method.ident == 'y':  # yescrypt
+        if rounds is not None:
+            if not 1 <= rounds <= 11:
+                raise ValueError('rounds out of the range 1 to 11')
+        else:
+            rounds = 5
+        s += 'j' + ('75', '85', '7T', '8T', '9T', 'AT', 'BT', 'CT', 'DT', 'ET', 'FT')[rounds - 1] + '$'
+    elif method.ident and method.ident[0] == '2':  # Blowfish variants
         if rounds is None:
             log_rounds = 12
         else:
@@ -102,6 +109,10 @@ def _add_method(name, *args, rounds=None):
         return True
     return False
 
+# Supported by libxcrypt.  Strongest hashing method currently supported.
+_add_method('YESCRYPT', 'y', 24, 75, rounds=1)
+
+# SHA-2 based methods.
 _add_method('SHA512', '6', 16, 106)
 _add_method('SHA256', '5', 16, 63)
 
diff --git a/Lib/test/test_crypt.py b/Lib/test/test_crypt.py
index 5dc83b4ecbfa008..7d22c87496180dd 100644
--- a/Lib/test/test_crypt.py
+++ b/Lib/test/test_crypt.py
@@ -88,7 +88,29 @@ def test_blowfish_rounds(self):
             cr2 = crypt.crypt('mypassword', cr)
             self.assertEqual(cr2, cr)
 
+    @unittest.skipUnless(
+        crypt and crypt.METHOD_YESCRYPT in crypt.methods, 'requires support of yescrypt'
+    )
+    def test_yescrypt_rounds(self):
+        for rounds in range(1, 11):
+            enc_rounds = 'j' + ('75', '85', '7T', '8T', '9T', 'AT', 'BT', 'CT', 'DT', 'ET', 'FT')[rounds - 1]
+            salt = crypt.mksalt(crypt.METHOD_YESCRYPT, rounds=rounds)
+            self.assertIn('$%s$' % enc_rounds, salt)
+            self.assertEqual(len(salt) - crypt.METHOD_YESCRYPT.salt_chars, 7)
+            cr = crypt.crypt('mypassword', salt)
+            self.assertTrue(cr)
+            cr2 = crypt.crypt('mypassword', cr)
+            self.assertEqual(cr2, cr)
+
     def test_invalid_rounds(self):
+        if crypt.METHOD_YESCRYPT in crypt.methods:
+            with self.assertRaises(TypeError):
+                crypt.mksalt(crypt.METHOD_YESCRYPT, rounds='4096')
+            with self.assertRaises(TypeError):
+                crypt.mksalt(crypt.METHOD_YESCRYPT, rounds=4096.0)
+            for rounds in (0, -1, 1000, 1<<999):
+                with self.assertRaises(ValueError):
+                    crypt.mksalt(crypt.METHOD_YESCRYPT, rounds=rounds)
         for method in (crypt.METHOD_SHA256, crypt.METHOD_SHA512,
                        crypt.METHOD_BLOWFISH):
             with self.assertRaises(TypeError):
diff --git a/Misc/NEWS.d/next/Library/2021-06-04-11-19-28.bpo-44309.PBcd1f.rst b/Misc/NEWS.d/next/Library/2021-06-04-11-19-28.bpo-44309.PBcd1f.rst
new file mode 100644
index 000000000000000..0056ee81e23ea88
--- /dev/null
+++ b/Misc/NEWS.d/next/Library/2021-06-04-11-19-28.bpo-44309.PBcd1f.rst
@@ -0,0 +1 @@
+Add support for the yescrypt hashing method in the crypt module.
\ No newline at end of file