diff --git a/stdlib/2/hashlib.pyi b/stdlib/2/hashlib.pyi
index 95f2b82f6..375cc59aa 100644
--- a/stdlib/2/hashlib.pyi
+++ b/stdlib/2/hashlib.pyi
@@ -1,24 +1,26 @@
 # Stubs for hashlib (Python 2)
 
-from typing import Tuple
+from typing import Tuple, Union
+
+_DataType = Union[str, bytearray, buffer, memoryview]
 
 class _hash(object):
     # This is not actually in the module namespace.
     digest_size = 0
     block_size = 0
-    def update(self, arg: str) -> None: ...
+    def update(self, arg: _DataType) -> None: ...
     def digest(self) -> str: ...
     def hexdigest(self) -> str: ...
     def copy(self) -> _hash: ...
 
 def new(name: str, data: str = ...) -> _hash: ...
 
-def md5(s: str = ...) -> _hash: ...
-def sha1(s: str = ...) -> _hash: ...
-def sha224(s: str = ...) -> _hash: ...
-def sha256(s: str = ...) -> _hash: ...
-def sha384(s: str = ...) -> _hash: ...
-def sha512(s: str = ...) -> _hash: ...
+def md5(s: _DataType = ...) -> _hash: ...
+def sha1(s: _DataType = ...) -> _hash: ...
+def sha224(s: _DataType = ...) -> _hash: ...
+def sha256(s: _DataType = ...) -> _hash: ...
+def sha384(s: _DataType = ...) -> _hash: ...
+def sha512(s: _DataType = ...) -> _hash: ...
 
 algorithms = ...  # type: Tuple[str, ...]
 algorithms_guaranteed = ...  # type: Tuple[str, ...]
diff --git a/stdlib/3/hashlib.pyi b/stdlib/3/hashlib.pyi
index 4d3709b20..fd47015d5 100644
--- a/stdlib/3/hashlib.pyi
+++ b/stdlib/3/hashlib.pyi
@@ -1,7 +1,9 @@
 # Stubs for hashlib
 
 from abc import abstractmethod, ABCMeta
-from typing import AbstractSet
+from typing import AbstractSet, Union
+
+_DataType = Union[bytes, bytearray, memoryview]
 
 class Hash(metaclass=ABCMeta):
     digest_size = ...  # type: int
@@ -13,7 +15,7 @@ class Hash(metaclass=ABCMeta):
     name = ...  # type: str
 
     @abstractmethod
-    def update(self, arg: bytes) -> None: ...
+    def update(self, arg: _DataType) -> None: ...
     @abstractmethod
     def digest(self) -> bytes: ...
     @abstractmethod
@@ -21,20 +23,18 @@ class Hash(metaclass=ABCMeta):
     @abstractmethod
     def copy(self) -> 'Hash': ...
 
-def md5(arg: bytes = ...) -> Hash: ...
-def sha1(arg: bytes = ...) -> Hash: ...
-def sha224(arg: bytes = ...) -> Hash: ...
-def sha256(arg: bytes = ...) -> Hash: ...
-def sha384(arg: bytes = ...) -> Hash: ...
-def sha512(arg: bytes = ...) -> Hash: ...
+def md5(arg: _DataType = ...) -> Hash: ...
+def sha1(arg: _DataType = ...) -> Hash: ...
+def sha224(arg: _DataType = ...) -> Hash: ...
+def sha256(arg: _DataType = ...) -> Hash: ...
+def sha384(arg: _DataType = ...) -> Hash: ...
+def sha512(arg: _DataType = ...) -> Hash: ...
 
-def new(name: str, data: bytes = ...) -> Hash: ...
+def new(name: str, data: _DataType = ...) -> Hash: ...
 
 # New in version 3.2
 algorithms_guaranteed = ...  # type: AbstractSet[str]
 algorithms_available = ...  # type: AbstractSet[str]
 
 # New in version 3.4
-# TODO The documentation says "password and salt are interpreted as buffers of
-# bytes", should we declare something other than bytes here?
-def pbkdf2_hmac(name: str, password: bytes, salt: bytes, rounds: int, dklen: int = ...) -> bytes: ...
+def pbkdf2_hmac(name: str, password: _DataType, salt: _DataType, rounds: int, dklen: int = ...) -> bytes: ...