diff --git a/Misc/NEWS.d/next/Library/2021-07-20-21-51-35.bpo-42854.ThuDMI.rst b/Misc/NEWS.d/next/Library/2021-07-20-21-51-35.bpo-42854.ThuDMI.rst
new file mode 100644
index 00000000000000..33cbb63a5e14b8
--- /dev/null
+++ b/Misc/NEWS.d/next/Library/2021-07-20-21-51-35.bpo-42854.ThuDMI.rst
@@ -0,0 +1,3 @@
+Fixed a bug in the :mod:`_ssl` module that was throwing :exc:`OverflowError`
+when using :meth:`_ssl._SSLSocket.write` and :meth:`_ssl._SSLSocket.read`
+for a big value of the ``len`` parameter. Patch by Pablo Galindo
diff --git a/Modules/_ssl.c b/Modules/_ssl.c
index ad5269d7b07b63..84cc3697b07063 100644
--- a/Modules/_ssl.c
+++ b/Modules/_ssl.c
@@ -2346,7 +2346,7 @@ _ssl__SSLSocket_write_impl(PySSLSocket *self, Py_buffer *b)
 
     do {
         PySSL_BEGIN_ALLOW_THREADS
-        retval = SSL_write_ex(self->ssl, b->buf, (int)b->len, &count);
+        retval = SSL_write_ex(self->ssl, b->buf, (size_t)b->len, &count);
         err = _PySSL_errno(retval == 0, self->ssl, retval);
         PySSL_END_ALLOW_THREADS
         self->err = err;
@@ -2418,7 +2418,7 @@ _ssl__SSLSocket_pending_impl(PySSLSocket *self)
 
 /*[clinic input]
 _ssl._SSLSocket.read
-    size as len: int
+    size as len: Py_ssize_t
     [
     buffer: Py_buffer(accept={rwbuffer})
     ]
@@ -2428,9 +2428,9 @@ Read up to size bytes from the SSL socket.
 [clinic start generated code]*/
 
 static PyObject *
-_ssl__SSLSocket_read_impl(PySSLSocket *self, int len, int group_right_1,
-                          Py_buffer *buffer)
-/*[clinic end generated code: output=00097776cec2a0af input=ff157eb918d0905b]*/
+_ssl__SSLSocket_read_impl(PySSLSocket *self, Py_ssize_t len,
+                          int group_right_1, Py_buffer *buffer)
+/*[clinic end generated code: output=49b16e6406023734 input=ec48bf622be1c4a1]*/
 {
     PyObject *dest = NULL;
     char *mem;
@@ -2498,7 +2498,7 @@ _ssl__SSLSocket_read_impl(PySSLSocket *self, int len, int group_right_1,
 
     do {
         PySSL_BEGIN_ALLOW_THREADS
-        retval = SSL_read_ex(self->ssl, mem, len, &count);
+        retval = SSL_read_ex(self->ssl, mem, (size_t)len, &count);
         err = _PySSL_errno(retval == 0, self->ssl, retval);
         PySSL_END_ALLOW_THREADS
         self->err = err;
diff --git a/Modules/clinic/_ssl.c.h b/Modules/clinic/_ssl.c.h
index b153c30cf39ae0..b59b129af8a095 100644
--- a/Modules/clinic/_ssl.c.h
+++ b/Modules/clinic/_ssl.c.h
@@ -271,25 +271,25 @@ PyDoc_STRVAR(_ssl__SSLSocket_read__doc__,
     {"read", (PyCFunction)_ssl__SSLSocket_read, METH_VARARGS, _ssl__SSLSocket_read__doc__},
 
 static PyObject *
-_ssl__SSLSocket_read_impl(PySSLSocket *self, int len, int group_right_1,
-                          Py_buffer *buffer);
+_ssl__SSLSocket_read_impl(PySSLSocket *self, Py_ssize_t len,
+                          int group_right_1, Py_buffer *buffer);
 
 static PyObject *
 _ssl__SSLSocket_read(PySSLSocket *self, PyObject *args)
 {
     PyObject *return_value = NULL;
-    int len;
+    Py_ssize_t len;
     int group_right_1 = 0;
     Py_buffer buffer = {NULL, NULL};
 
     switch (PyTuple_GET_SIZE(args)) {
         case 1:
-            if (!PyArg_ParseTuple(args, "i:read", &len)) {
+            if (!PyArg_ParseTuple(args, "n:read", &len)) {
                 goto exit;
             }
             break;
         case 2:
-            if (!PyArg_ParseTuple(args, "iw*:read", &len, &buffer)) {
+            if (!PyArg_ParseTuple(args, "nw*:read", &len, &buffer)) {
                 goto exit;
             }
             group_right_1 = 1;
@@ -1358,4 +1358,4 @@ _ssl_enum_crls(PyObject *module, PyObject *const *args, Py_ssize_t nargs, PyObje
 #ifndef _SSL_ENUM_CRLS_METHODDEF
     #define _SSL_ENUM_CRLS_METHODDEF
 #endif /* !defined(_SSL_ENUM_CRLS_METHODDEF) */
-/*[clinic end generated code: output=3b6f4471fb187d85 input=a9049054013a1b77]*/
+/*[clinic end generated code: output=5a7d7bf5cf8ee092 input=a9049054013a1b77]*/