diff --git a/moto/autoscaling/models.py b/moto/autoscaling/models.py
index d7f0db620..5a044c038 100644
--- a/moto/autoscaling/models.py
+++ b/moto/autoscaling/models.py
@@ -80,6 +80,10 @@ class FakeLaunchConfiguration(object):
         )
         return config
 
+    def delete(self, region_name):
+        backend = autoscaling_backends[region_name]
+        backend.delete_launch_configuration(self.name)
+
     @property
     def physical_resource_id(self):
         return self.name
@@ -167,6 +171,10 @@ class FakeAutoScalingGroup(object):
         )
         return group
 
+    def delete(self, region_name):
+        backend = autoscaling_backends[region_name]
+        backend.delete_autoscaling_group(self.name)
+
     @property
     def physical_resource_id(self):
         return self.name
diff --git a/moto/cloudformation/models.py b/moto/cloudformation/models.py
index cd99856f5..d8793b8ea 100644
--- a/moto/cloudformation/models.py
+++ b/moto/cloudformation/models.py
@@ -52,6 +52,10 @@ class FakeStack(object):
         self.resource_map.update(json.loads(template))
         self.output_map = self._create_output_map()
 
+    def delete(self):
+        self.resource_map.delete()
+        self.status = 'DELETE_COMPLETE'
+
 
 class CloudFormationBackend(BaseBackend):
 
@@ -112,13 +116,14 @@ class CloudFormationBackend(BaseBackend):
         if name_or_stack_id in self.stacks:
             # Delete by stack id
             stack = self.stacks.pop(name_or_stack_id, None)
-            stack.status = 'DELETE_COMPLETE'
+            stack.delete()
             self.deleted_stacks[stack.stack_id] = stack
             return self.stacks.pop(name_or_stack_id, None)
         else:
             # Delete by stack name
-            stack_to_delete = [stack for stack in self.stacks.values() if stack.name == name_or_stack_id][0]
-            self.delete_stack(stack_to_delete.stack_id)
+            for stack in list(self.stacks.values()):
+                if stack.name == name_or_stack_id:
+                    self.delete_stack(stack.stack_id)
 
 
 cloudformation_backends = {}
diff --git a/moto/cloudformation/parsing.py b/moto/cloudformation/parsing.py
index ebdd83634..32b9f351f 100644
--- a/moto/cloudformation/parsing.py
+++ b/moto/cloudformation/parsing.py
@@ -374,6 +374,11 @@ class ResourceMap(collections.Mapping):
                 changed_resource = parse_and_update_resource(resource_name, resource_json, self, self._region_name)
                 self._parsed_resources[resource_name] = changed_resource
 
+    def delete(self):
+        for resource in self.resources:
+            parsed_resource = self._parsed_resources.pop(resource)
+            parsed_resource.delete(self._region_name)
+
 
 class OutputMap(collections.Mapping):
     def __init__(self, resources, template):