diff --git a/packages/@aws-cdk/aws-ec2/README.md b/packages/@aws-cdk/aws-ec2/README.md
index 1a442e104e4b0..3b902e5cb8c75 100644
--- a/packages/@aws-cdk/aws-ec2/README.md
+++ b/packages/@aws-cdk/aws-ec2/README.md
@@ -538,6 +538,9 @@ examples of things you might want to use:
 > `cdk.context.json`, or use the `cdk context` command. For more information, see
 > [Runtime Context](https://docs.aws.amazon.com/cdk/latest/guide/context.html) in the CDK
 > developer guide.
+>
+> `MachineImage.genericLinux()`, `MachineImage.genericWindows()` will use `CfnMapping` in
+> an agnostic stack.
 
 ## Special VPC configurations
 
diff --git a/packages/@aws-cdk/aws-ec2/lib/machine-image.ts b/packages/@aws-cdk/aws-ec2/lib/machine-image.ts
index 1871fc1e75ac5..df4a1eece07e0 100644
--- a/packages/@aws-cdk/aws-ec2/lib/machine-image.ts
+++ b/packages/@aws-cdk/aws-ec2/lib/machine-image.ts
@@ -1,6 +1,6 @@
 import * as ssm from '@aws-cdk/aws-ssm';
 import * as cxschema from '@aws-cdk/cloud-assembly-schema';
-import { ContextProvider, Stack, Token } from '@aws-cdk/core';
+import { ContextProvider, CfnMapping, Aws, Stack, Token } from '@aws-cdk/core';
 import * as cxapi from '@aws-cdk/cx-api';
 import { UserData } from './user-data';
 import { WindowsVersion } from './windows-versions';
@@ -367,24 +367,33 @@ export interface GenericWindowsImageProps {
  * manually specify an AMI map.
  */
 export class GenericLinuxImage implements IMachineImage {
-  constructor(private readonly amiMap: {[region: string]: string}, private readonly props: GenericLinuxImageProps = {}) {
+  constructor(private readonly amiMap: { [region: string]: string }, private readonly props: GenericLinuxImageProps = {}) {
   }
 
   public getImage(scope: Construct): MachineImageConfig {
+    const userData = this.props.userData ?? UserData.forLinux();
+    const osType = OperatingSystemType.LINUX;
     const region = Stack.of(scope).region;
     if (Token.isUnresolved(region)) {
-      throw new Error('Unable to determine AMI from AMI map since stack is region-agnostic');
+      const mapping: { [k1: string]: { [k2: string]: any } } = {};
+      for (const [rgn, ami] of Object.entries(this.amiMap)) {
+        mapping[rgn] = { ami };
+      }
+      const amiMap = new CfnMapping(scope, 'AmiMap', { mapping });
+      return {
+        imageId: amiMap.findInMap(Aws.REGION, 'ami'),
+        userData,
+        osType,
+      };
     }
-
-    const ami = region !== 'test-region' ? this.amiMap[region] : 'ami-12345';
-    if (!ami) {
+    const imageId = region !== 'test-region' ? this.amiMap[region] : 'ami-12345';
+    if (!imageId) {
       throw new Error(`Unable to find AMI in AMI map: no AMI specified for region '${region}'`);
     }
-
     return {
-      imageId: ami,
-      userData: this.props.userData ?? UserData.forLinux(),
-      osType: OperatingSystemType.LINUX,
+      imageId,
+      userData,
+      osType,
     };
   }
 }
@@ -399,20 +408,29 @@ export class GenericWindowsImage implements IMachineImage {
   }
 
   public getImage(scope: Construct): MachineImageConfig {
+    const userData = this.props.userData ?? UserData.forWindows();
+    const osType = OperatingSystemType.WINDOWS;
     const region = Stack.of(scope).region;
     if (Token.isUnresolved(region)) {
-      throw new Error('Unable to determine AMI from AMI map since stack is region-agnostic');
+      const mapping: { [k1: string]: { [k2: string]: any } } = {};
+      for (const [rgn, ami] of Object.entries(this.amiMap)) {
+        mapping[rgn] = { ami };
+      }
+      const amiMap = new CfnMapping(scope, 'AmiMap', { mapping });
+      return {
+        imageId: amiMap.findInMap(Aws.REGION, 'ami'),
+        userData,
+        osType,
+      };
     }
-
-    const ami = region !== 'test-region' ? this.amiMap[region] : 'ami-12345';
-    if (!ami) {
+    const imageId = region !== 'test-region' ? this.amiMap[region] : 'ami-12345';
+    if (!imageId) {
       throw new Error(`Unable to find AMI in AMI map: no AMI specified for region '${region}'`);
     }
-
     return {
-      imageId: ami,
-      userData: this.props.userData ?? UserData.forWindows(),
-      osType: OperatingSystemType.WINDOWS,
+      imageId,
+      userData,
+      osType,
     };
   }
 }
diff --git a/packages/@aws-cdk/aws-ec2/test/machine-image.test.ts b/packages/@aws-cdk/aws-ec2/test/machine-image.test.ts
index 2fcf7e2980be9..43e6dbdcd88cf 100644
--- a/packages/@aws-cdk/aws-ec2/test/machine-image.test.ts
+++ b/packages/@aws-cdk/aws-ec2/test/machine-image.test.ts
@@ -1,3 +1,4 @@
+import { expect as cdkExpect, matchTemplate, MatchStyle } from '@aws-cdk/assert';
 import { App, Stack } from '@aws-cdk/core';
 import * as ec2 from '../lib';
 
@@ -11,6 +12,43 @@ beforeEach(() => {
   });
 });
 
+test('can make and use a Linux image', () => {
+  // WHEN
+  const image = new ec2.GenericLinuxImage({
+    testregion: 'ami-1234',
+  });
+
+  // THEN
+  const details = image.getImage(stack);
+  expect(details.imageId).toEqual('ami-1234');
+  expect(details.osType).toEqual(ec2.OperatingSystemType.LINUX);
+});
+
+test('can make and use a Linux image in agnostic stack', () => {
+  // WHEN
+  app = new App();
+  stack = new Stack(app, 'Stack');
+  const image = new ec2.GenericLinuxImage({
+    testregion: 'ami-1234',
+  });
+
+  // THEN
+  const details = image.getImage(stack);
+  const expected = {
+    Mappings: {
+      AmiMap: {
+        testregion: {
+          ami: 'ami-1234',
+        },
+      },
+    },
+  };
+
+  cdkExpect(stack).to(matchTemplate(expected, MatchStyle.EXACT));
+  expect(stack.resolve(details.imageId)).toEqual({ 'Fn::FindInMap': ['AmiMap', { Ref: 'AWS::Region' }, 'ami'] });
+  expect(details.osType).toEqual(ec2.OperatingSystemType.LINUX);
+});
+
 test('can make and use a Windows image', () => {
   // WHEN
   const image = new ec2.GenericWindowsImage({
@@ -23,6 +61,31 @@ test('can make and use a Windows image', () => {
   expect(details.osType).toEqual(ec2.OperatingSystemType.WINDOWS);
 });
 
+test('can make and use a Windows image in agnostic stack', () => {
+  // WHEN
+  app = new App();
+  stack = new Stack(app, 'Stack');
+  const image = new ec2.GenericWindowsImage({
+    testregion: 'ami-1234',
+  });
+
+  // THEN
+  const details = image.getImage(stack);
+  const expected = {
+    Mappings: {
+      AmiMap: {
+        testregion: {
+          ami: 'ami-1234',
+        },
+      },
+    },
+  };
+
+  cdkExpect(stack).to(matchTemplate(expected, MatchStyle.EXACT));
+  expect(stack.resolve(details.imageId)).toEqual({ 'Fn::FindInMap': ['AmiMap', { Ref: 'AWS::Region' }, 'ami'] });
+  expect(details.osType).toEqual(ec2.OperatingSystemType.WINDOWS);
+});
+
 test('can make and use a Generic SSM image', () => {
   // WHEN
   const image = new ec2.GenericSSMParameterImage('testParam', ec2.OperatingSystemType.LINUX);