diff --git a/swh/web/api/apiresponse.py b/swh/web/api/apiresponse.py
--- a/swh/web/api/apiresponse.py
+++ b/swh/web/api/apiresponse.py
@@ -13,7 +13,10 @@
 from swh.storage.exc import StorageDBError, StorageAPIError
 
 from swh.web.api import utils
-from swh.web.common.exc import NotFoundExc, ForbiddenExc, BadInputExc
+from swh.web.common.exc import (
+    NotFoundExc, ForbiddenExc,
+    BadInputExc, LargePayloadExc
+)
 from swh.web.common.utils import shorten_path, gen_path_info
 from swh.web.config import get_config
 
@@ -165,6 +168,8 @@
         error_code = 404
     elif isinstance(error, ForbiddenExc):
         error_code = 403
+    elif isinstance(error, LargePayloadExc):
+        error_code = 413
     elif isinstance(error, StorageDBError):
         error_code = 503
     elif isinstance(error, StorageAPIError):
diff --git a/swh/web/api/views/identifiers.py b/swh/web/api/views/identifiers.py
--- a/swh/web/api/views/identifiers.py
+++ b/swh/web/api/views/identifiers.py
@@ -10,6 +10,7 @@
 )
 from swh.web.api.apidoc import api_doc, format_docstring
 from swh.web.api.apiurls import api_route
+from swh.web.common.exc import LargePayloadExc
 
 
 @api_route(r'/resolve/(?P<swh_id>.*)/',
@@ -84,6 +85,11 @@
                 the pid is present, False otherwise)
 
     """
+    limit = 1000
+    if len(request.data) > limit:
+        raise LargePayloadExc('The maximum number of PIDs this endpoint can '
+                              'receive is %s' % limit)
+
     persistent_ids = [get_persistent_identifier(pid)
                       for pid in request.data]
 
diff --git a/swh/web/common/exc.py b/swh/web/common/exc.py
--- a/swh/web/common/exc.py
+++ b/swh/web/common/exc.py
@@ -44,11 +44,21 @@
     pass
 
 
+class LargePayloadExc(Exception):
+    """The input size is too large.
+
+    Example: Asking to resolve 10000 persistent identifier when the limit
+    is 1000.
+    """
+    pass
+
+
 http_status_code_message = {
     400: 'Bad Request',
     401: 'Unauthorized',
     403: 'Access Denied',
     404: 'Resource not found',
+    413: 'Payload Too Large',
     500: 'Internal Server Error',
     501: 'Not Implemented',
     502: 'Bad Gateway',
diff --git a/swh/web/tests/api/views/test_identifiers.py b/swh/web/tests/api/views/test_identifiers.py
--- a/swh/web/tests/api/views/test_identifiers.py
+++ b/swh/web/tests/api/views/test_identifiers.py
@@ -140,3 +140,22 @@
                             HTTP_ACCEPT='application/json')
 
     assert resp2.status_code == 400, resp.data
+
+
+def test_api_known_raises_large_payload_error(api_client):
+    random_pid = 'swh:1:cnt:8068d0075010b590762c6cb5682ed53cb3c13deb'
+    limit = 10000
+    err_msg = 'The maximum number of PIDs this endpoint can receive is 1000'
+
+    pids = [random_pid for i in range(limit)]
+
+    url = reverse('api-1-swh-pid-known')
+    resp = api_client.post(url, data=pids, format='json',
+                           HTTP_ACCEPT='application/json')
+
+    assert resp.status_code == 413, resp.data
+    assert resp['Content-Type'] == 'application/json'
+    assert resp.data == {
+        'exception': 'LargePayloadExc',
+        'reason': err_msg
+    }