diff --git a/spec/schemas/ml._common.yaml b/spec/schemas/ml._common.yaml
index 46cffc9f3..b142e40ff 100644
--- a/spec/schemas/ml._common.yaml
+++ b/spec/schemas/ml._common.yaml
@@ -19,13 +19,48 @@ components:
       required:
         - query
         - size
+    BaseResponse:
+      type: object
+      properties:
+        _version:
+          type: integer
+          description: The version.
+        _seq_no:
+          type: integer
+          description: The sequence number.
+        _primary_term:
+          type: integer
+          description: The primary term.
     SearchModelsResponse:
       type: object
       properties:
+        took:
+          type: integer
+          description: The time taken to execute the search.
+        timed_out:
+          type: boolean
+          description: Whether the search timed out.
+        _shards:
+          $ref: '#/components/schemas/SearchModelsShardsResponse'
         hits:
           $ref: '#/components/schemas/SearchModelsHits'
       required:
         - hits
+    SearchModelsShardsResponse:
+      type: object
+      properties:
+        total:
+          type: integer
+          description: The total number of shards.
+        successful:
+          type: integer
+          description: The number of successful shards.
+        skipped:
+          type: integer
+          description: The number of skipped shards.
+        failed:
+          type: integer
+          description: The number of failed shards.
     SearchModelsHits:
       type: object
       properties:
@@ -35,6 +70,9 @@ components:
           type: array
           items:
             $ref: '#/components/schemas/SearchModelsHitsHit'
+        max_score:
+          type: number
+          description: The maximum score.
       required:
         - hits
         - total
@@ -51,20 +89,75 @@ components:
         - relation
         - value
     SearchModelsHitsHit:
+      allOf:
+        - $ref: '#/components/schemas/BaseResponse'
+        - type: object
+          properties:
+            _index:
+              type: string
+              description: The index.
+            _id:
+              type: string
+              description: The hit ID.
+            _score:
+              type: number
+              description: The score.
+            _source:
+              $ref: '#/components/schemas/Source'
+            model_id:
+              type: string
+              description: The model ID.
+          required:
+            - _score
+    Source:
       type: object
       properties:
-        _index:
+        last_deployed_time:
+          type: number
+          description: The last deployed time.
+        model_version:
           type: string
-          description: The index.
-        _id:
+          description: The model version.
+        created_time:
+          type: number
+          description: The created time.
+        deploy_to_all_nodes:
+          type: boolean
+          description: Whether to deploy to all nodes.
+        is_hidden:
+          type: boolean
+          description: Whether the model is hidden.
+        description:
           type: string
-          description: The hit ID.
-        model_id:
+          description: The model description.
+        model_state:
           type: string
-          description: The model ID.
-      required:
-        - _id
-        - model_id
+          description: The model state.
+        planning_worker_node_count:
+          type: number
+          description: The planning worker node count.
+        last_updated_time:
+          type: number
+          description: The last updated time.
+        name:
+          type: string
+          description: The model name.
+        connector_id:
+          type: string
+          description: The connector ID.
+        current_worker_node_count:
+          type: number
+          description: The current worker node count.
+        model_group_id:
+          type: string
+          description: The model group ID.
+        planning_worker_nodes:
+          type: array
+          items:
+            $ref: '_common.yaml#/components/schemas/NodeIds'
+        algorithm:
+          type: string
+          description: The algorithm.
     ModelGroupRegistration:
       type: object
       properties:
diff --git a/tests/plugins/ml/ml/models.yaml b/tests/plugins/ml/ml/models.yaml
index ce087654f..a8b8fc30d 100644
--- a/tests/plugins/ml/ml/models.yaml
+++ b/tests/plugins/ml/ml/models.yaml
@@ -22,6 +22,23 @@ chapters:
       status: 200
     output:
       task_id: payload.task_id
+  - synopsis: Search model.
+    id: search_model
+    path: /_plugins/_ml/models/_search
+    method: GET
+    request:
+      payload:
+        query:
+          match_all: {}
+        size: 1000
+    response:
+      status: 200
+      payload:
+        hits:
+          hits:
+            - _score: 1
+    output:
+      search_id: payload.hits.hits[0]._id
   - synopsis: Wait to get completed task.
     id: get_completed_task
     path: /_plugins/_ml/tasks/{task_id}
diff --git a/tests/plugins/ml/ml/tasks.yaml b/tests/plugins/ml/ml/tasks.yaml
new file mode 100644
index 000000000..7a1720493
--- /dev/null
+++ b/tests/plugins/ml/ml/tasks.yaml
@@ -0,0 +1,32 @@
+$schema: ../../../../json_schemas/test_story.schema.yaml
+
+description: Test the creation of tasks.
+distributions:
+  excluded:
+    - amazon-managed
+    - amazon-serverless
+version: '>= 2.11'
+warnings:
+  multiple-paths-detected: false
+chapters:
+  - synopsis: Register model.
+    id: register_model
+    path: /_plugins/_ml/models/_register
+    method: POST
+    request:
+      payload:
+        name: huggingface/sentence-transformers/msmarco-distilbert-base-tas-b
+        version: 1.0.1
+        model_format: TORCH_SCRIPT
+    response:
+      status: 200
+    output:
+      task_id: payload.task_id
+  - synopsis: Delete task.
+    id: delete_task
+    path: /_plugins/_ml/tasks/{task_id}
+    method: DELETE
+    parameters:
+      task_id: ${register_model.task_id}
+    response:
+      status: 200
\ No newline at end of file