diff --git a/Lib/_pyio.py b/Lib/_pyio.py
index a5d6135..35dea41 100644
--- a/Lib/_pyio.py
+++ b/Lib/_pyio.py
@@ -14,6 +14,7 @@
 
 import io
 from io import (__all__, SEEK_SET, SEEK_CUR, SEEK_END)
+from errno import EINTR
 
 # open() uses st_blksize whenever we can
 DEFAULT_BUFFER_SIZE = 8 * 1024  # bytes
@@ -943,7 +944,12 @@
             current_size = 0
             while True:
                 # Read until EOF or until read() would block.
-                chunk = self.raw.read()
+                try:
+                    chunk = self.raw.read()
+                except IOError as e:
+                    if e.errno != EINTR:
+                        raise
+                    continue
                 if chunk in empty_values:
                     nodata_val = chunk
                     break
@@ -962,7 +968,12 @@
         chunks = [buf[pos:]]
         wanted = max(self.buffer_size, n)
         while avail < n:
-            chunk = self.raw.read(wanted)
+            try:
+                chunk = self.raw.read(wanted)
+            except IOError as e:
+                if e.errno != EINTR:
+                    raise
+                continue
             if chunk in empty_values:
                 nodata_val = chunk
                 break
@@ -991,7 +1002,14 @@
         have = len(self._read_buf) - self._read_pos
         if have < want or have <= 0:
             to_read = self.buffer_size - have
-            current = self.raw.read(to_read)
+            while True:
+                try:
+                    current = self.raw.read(to_read)
+                except IOError as e:
+                    if e.errno != EINTR:
+                        raise
+                    continue
+                break
             if current:
                 self._read_buf = self._read_buf[self._read_pos:] + current
                 self._read_pos = 0
@@ -1098,7 +1116,12 @@
         written = 0
         try:
             while self._write_buf:
-                n = self.raw.write(self._write_buf)
+                try:
+                    n = self.raw.write(self._write_buf)
+                except IOError as e:
+                    if e.errno != EINTR:
+                        raise
+                    continue
                 if n > len(self._write_buf) or n < 0:
                     raise IOError("write() returned incorrect number of bytes")
                 del self._write_buf[:n]
diff --git a/Lib/test/test_io.py b/Lib/test/test_io.py
index a25d9af..b665a6c 100644
--- a/Lib/test/test_io.py
+++ b/Lib/test/test_io.py
@@ -2622,7 +2622,8 @@
     @unittest.skipUnless(threading, 'Threading required for this test.')
     def check_interrupted_write(self, item, bytes, **fdopen_kwargs):
         """Check that a partial write, when it gets interrupted, properly
-        invokes the signal handler."""
+        invokes the signal handler, and bubbles up the exception raised
+        in the latter."""
         read_results = []
         def _read():
             s = os.read(r, 1)
@@ -2701,6 +2702,98 @@
     def test_reentrant_write_text(self):
         self.check_reentrant_write("xy", mode="w", encoding="ascii")
 
+    def check_interrupted_read_retry(self, decode, **fdopen_kwargs):
+        """Check that a buffered read, when it gets interrupted (either
+        returning a partial result or EINTR), properly invokes the signal
+        handler and retries if the latter returned successfully."""
+        r, w = os.pipe()
+        fdopen_kwargs["closefd"] = False
+        def alarm_handler(sig, frame):
+            os.write(w, b"bar")
+        signal.signal(signal.SIGALRM, alarm_handler)
+        try:
+            rio = self.io.open(r, **fdopen_kwargs)
+            os.write(w, b"foo")
+            signal.alarm(1)
+            # Expected behaviour:
+            # - first raw read() returns partial b"foo"
+            # - second raw read() returns EINTR
+            # - third raw read() returns b"bar"
+            self.assertEqual(decode(rio.read(6)), "foobar")
+        finally:
+            rio.close()
+            os.close(w)
+            os.close(r)
+
+    def test_interrupterd_read_retry_buffered(self):
+        self.check_interrupted_read_retry(lambda x: x.decode('latin1'),
+                                          mode="rb")
+
+    def test_interrupterd_read_retry_text(self):
+        self.check_interrupted_read_retry(lambda x: x,
+                                          mode="r")
+
+    @unittest.skipUnless(threading, 'Threading required for this test.')
+    def check_interrupted_write_retry(self, item, **fdopen_kwargs):
+        """Check that a buffered write, when it gets interrupted (either
+        returning a partial result or EINTR), properly invokes the signal
+        handler and retries if the latter returned successfully."""
+        select = support.import_module("select")
+        # A quantity that exceeds the buffer size of an anonymous pipe's
+        # write end.
+        N = 1024 * 1024
+        r, w = os.pipe()
+        fdopen_kwargs["closefd"] = False
+        # We need a separate thread to read from the pipe and allow the
+        # write() to finish.  This thread is started after the SIGALRM is
+        # received (forcing a first EINTR in write()).
+        read_results = []
+        write_finished = False
+        def _read():
+            while not write_finished:
+                while r in select.select([r], [], [], 1.0)[0]:
+                    s = os.read(r, 1024)
+                    read_results.append(s)
+        t = threading.Thread(target=_read)
+        t.daemon = True
+        def alarm1(sig, frame):
+            signal.signal(signal.SIGALRM, alarm2)
+            signal.alarm(1)
+        def alarm2(sig, frame):
+            t.start()
+        signal.signal(signal.SIGALRM, alarm1)
+        try:
+            wio = self.io.open(w, **fdopen_kwargs)
+            signal.alarm(1)
+            # Expected behaviour:
+            # - first raw write() is partial (because of the limited pipe buffer
+            #   and the first alarm)
+            # - second raw write() returns EINTR (because of the second alarm)
+            # - subsequent write()s are successful (either partial or complete)
+            self.assertEqual(N, wio.write(item * N))
+            wio.flush()
+            write_finished = True
+            t.join()
+            self.assertEqual(N, sum(len(x) for x in read_results))
+        finally:
+            write_finished = True
+            os.close(w)
+            os.close(r)
+            # This is deliberate. If we didn't close the file descriptor
+            # before closing wio, wio would try to flush its internal
+            # buffer, and could block (in case of failure).
+            try:
+                wio.close()
+            except IOError as e:
+                if e.errno != errno.EBADF:
+                    raise
+
+    def test_interrupterd_write_retry_buffered(self):
+        self.check_interrupted_write_retry(b"x", mode="wb")
+
+    def test_interrupterd_write_retry_text(self):
+        self.check_interrupted_write_retry("x", mode="w", encoding="latin1")
+
 
 class CSignalsTest(SignalsTest):
     io = io
diff --git a/Misc/NEWS b/Misc/NEWS
index e171032..65ea12a 100644
--- a/Misc/NEWS
+++ b/Misc/NEWS
@@ -24,6 +24,9 @@
 Library
 -------
 
+- Issue #10956: Buffered I/O classes retry reading or writing after a signal
+  has arrived and the handler returned successfully.
+
 - Issue #11224: Fixed a regression in tarfile that affected the file-like
   objects returned by TarFile.extractfile() regarding performance, memory
   consumption and failures with the stream interface.
diff --git a/Modules/_io/bufferedio.c b/Modules/_io/bufferedio.c
index 55c0a23..386a880 100644
--- a/Modules/_io/bufferedio.c
+++ b/Modules/_io/bufferedio.c
@@ -714,6 +714,39 @@
     return 0;
 }
 
+/* Return 1 if an EnvironmentError with errno == EINTR is set (and then
+   clears the error indicator), 0 otherwise.
+   Should only be called when PyErr_Occurred() is true.
+*/
+static int
+_trap_eintr(void)
+{
+    static PyObject *eintr_int = NULL;
+    PyObject *typ, *val, *tb;
+    PyEnvironmentErrorObject *env_err;
+
+    if (eintr_int == NULL) {
+        eintr_int = PyLong_FromLong(EINTR);
+        assert(eintr_int != NULL);
+    }
+    if (!PyErr_ExceptionMatches(PyExc_EnvironmentError))
+        return 0;
+    PyErr_Fetch(&typ, &val, &tb);
+    PyErr_NormalizeException(&typ, &val, &tb);
+    env_err = (PyEnvironmentErrorObject *) val;
+    assert(env_err != NULL);
+    if (env_err->myerrno != NULL &&
+        PyObject_RichCompareBool(env_err->myerrno, eintr_int, Py_EQ) > 0) {
+        Py_DECREF(typ);
+        Py_DECREF(val);
+        Py_XDECREF(tb);
+        return 1;
+    }
+    /* This silences any error set by PyObject_RichCompareBool() */
+    PyErr_Restore(typ, val, tb);
+    return 0;
+}
+
 /*
  * Shared methods and wrappers
  */
@@ -1269,7 +1302,14 @@
     memobj = PyMemoryView_FromBuffer(&buf);
     if (memobj == NULL)
         return -1;
-    res = PyObject_CallMethodObjArgs(self->raw, _PyIO_str_readinto, memobj, NULL);
+    /* NOTE: PyErr_SetFromErrno() calls PyErr_CheckSignals() when EINTR
+       occurs so we needn't do it ourselves.
+       We then retry reading, ignoring the signal if no handler has
+       raised (see issue #10956).
+    */
+    do {
+        res = PyObject_CallMethodObjArgs(self->raw, _PyIO_str_readinto, memobj, NULL);
+    } while (res == NULL && _trap_eintr());
     Py_DECREF(memobj);
     if (res == NULL)
         return -1;
@@ -1678,7 +1718,14 @@
     memobj = PyMemoryView_FromBuffer(&buf);
     if (memobj == NULL)
         return -1;
-    res = PyObject_CallMethodObjArgs(self->raw, _PyIO_str_write, memobj, NULL);
+    /* NOTE: PyErr_SetFromErrno() calls PyErr_CheckSignals() when EINTR
+       occurs so we needn't do it ourselves.
+       We then retry writing, ignoring the signal if no handler has
+       raised (see issue #10956).
+    */
+    do {
+        res = PyObject_CallMethodObjArgs(self->raw, _PyIO_str_write, memobj, NULL);
+    } while (res == NULL && _trap_eintr());
     Py_DECREF(memobj);
     if (res == NULL)
         return -1;