diff --git a/datasette/publish/cloudrun.py b/datasette/publish/cloudrun.py
index ff483bbb..91408287 100644
--- a/datasette/publish/cloudrun.py
+++ b/datasette/publish/cloudrun.py
@@ -2,6 +2,7 @@ from datasette import hookimpl
 import click
 import json
 import os
+import re
 from subprocess import check_call, check_output
 
 from .common import (
@@ -30,6 +31,11 @@ def publish_subcommand(publish):
         is_flag=True,
         help="Output the generated Dockerfile and metadata.json",
     )
+    @click.option(
+        "--memory",
+        callback=_validate_memory,
+        help="Memory to allocate in Cloud Run, e.g. 1Gi",
+    )
     def cloudrun(
         files,
         metadata,
@@ -52,6 +58,7 @@ def publish_subcommand(publish):
         service,
         spatialite,
         show_files,
+        memory,
     ):
         fail_if_publish_binary_not_installed(
             "gcloud", "Google Cloud", "https://cloud.google.com/sdk/"
@@ -127,8 +134,8 @@ def publish_subcommand(publish):
             image_id = "gcr.io/{project}/{name}".format(project=project, name=name)
             check_call("gcloud builds submit --tag {}".format(image_id), shell=True)
         check_call(
-            "gcloud run deploy --allow-unauthenticated --platform=managed --image {} {}".format(
-                image_id, service,
+            "gcloud run deploy --allow-unauthenticated --platform=managed --image {} {}{}".format(
+                image_id, service, " --memory {}".format(memory) if memory else ""
             ),
             shell=True,
         )
@@ -150,3 +157,9 @@ def get_existing_services():
         }
         for service in services
     ]
+
+
+def _validate_memory(ctx, param, value):
+    if re.match(r"^\d+(Gi|G|Mi|M)$", value) is None:
+        raise click.BadParameter("--memory should be a number then Gi/G/Mi/M e.g 1Gi")
+    return value
diff --git a/tests/test_publish_cloudrun.py b/tests/test_publish_cloudrun.py
index b035ca86..272dd68e 100644
--- a/tests/test_publish_cloudrun.py
+++ b/tests/test_publish_cloudrun.py
@@ -1,6 +1,7 @@
 from click.testing import CliRunner
 from datasette import cli
 from unittest import mock
+import pytest
 import json
 
 
@@ -98,6 +99,43 @@ def test_publish_cloudrun(mock_call, mock_output, mock_which):
         )
 
 
+@mock.patch("shutil.which")
+@mock.patch("datasette.publish.cloudrun.check_output")
+@mock.patch("datasette.publish.cloudrun.check_call")
+@pytest.mark.parametrize(
+    "memory,should_fail",
+    [["1Gi", False], ["2G", False], ["256Mi", False], ["4", True], ["GB", True],],
+)
+def test_publish_cloudrun_memory(
+    mock_call, mock_output, mock_which, memory, should_fail
+):
+    mock_output.return_value = "myproject"
+    mock_which.return_value = True
+    runner = CliRunner()
+    with runner.isolated_filesystem():
+        open("test.db", "w").write("data")
+        result = runner.invoke(
+            cli.cli,
+            ["publish", "cloudrun", "test.db", "--service", "test", "--memory", memory],
+        )
+        if should_fail:
+            assert 2 == result.exit_code
+            return
+        assert 0 == result.exit_code
+        tag = "gcr.io/{}/datasette".format(mock_output.return_value)
+        mock_call.assert_has_calls(
+            [
+                mock.call("gcloud builds submit --tag {}".format(tag), shell=True),
+                mock.call(
+                    "gcloud run deploy --allow-unauthenticated --platform=managed --image {} test --memory {}".format(
+                        tag, memory
+                    ),
+                    shell=True,
+                ),
+            ]
+        )
+
+
 @mock.patch("shutil.which")
 @mock.patch("datasette.publish.cloudrun.check_output")
 @mock.patch("datasette.publish.cloudrun.check_call")