diff --git a/moto/ecs/models.py b/moto/ecs/models.py
index e020e320..3ce7be8b 100644
--- a/moto/ecs/models.py
+++ b/moto/ecs/models.py
@@ -40,6 +40,10 @@ class Cluster(BaseObject):
         self.running_tasks_count = 0
         self.status = 'ACTIVE'
 
+    @property
+    def physical_resource_id(self):
+        return self.name
+
     @property
     def response_object(self):
         response_object = self.gen_response_object()
@@ -154,6 +158,10 @@ class Service(BaseObject):
         self.load_balancers = []
         self.pending_count = 0
 
+    @property
+    def physical_resource_id(self):
+        return self.arn
+
     @property
     def response_object(self):
         response_object = self.gen_response_object()