modelcontextprotocol
diff --git a/src/mcp/client/streamable_http.py b/src/mcp/client/streamable_http.py
@@ -479,10 +479,27 @@ async def _handle_message(session_message: SessionMessage) -> None:
                     )
 
                     async def handle_request_async():
-                        if is_resumption:
-                            await self._handle_resumption_request(ctx)
-                        else:
-                            await self._handle_post_request(ctx)
+                        try:
+                            if is_resumption:
+                                await self._handle_resumption_request(ctx)
+                            else:
+                                await self._handle_post_request(ctx)
+                        except httpx.HTTPError as exc:
+                            # Letting this escape into `tg` would crash the outer task group
+                            # from a different task than the one yielding the streams,
+                            # producing an uncatchable cancel-scope RuntimeError instead of
+                            # a connect error at the caller.
+                            logger.exception("Transport error handling request")
+                            if isinstance(message, JSONRPCRequest):
+                                error_data = ErrorData(
+                                    code=INTERNAL_ERROR,
+                                    message=f"Transport error: {exc}",
+                                )
+                                error_msg = SessionMessage(
+                                    JSONRPCError(jsonrpc="2.0", id=message.id, error=error_data)
+                                )
+                                with contextlib.suppress(anyio.BrokenResourceError, anyio.ClosedResourceError):
+                                    await read_stream_writer.send(error_msg)
 
                     # If this is a request, start a new task to handle it
                     if isinstance(message, JSONRPCRequest):

diff --git a/tests/issues/test_915_streamable_http_unreachable.py b/tests/issues/test_915_streamable_http_unreachable.py
@@ -0,0 +1,27 @@
+"""Regression test for issue #915.
+
+When a streamable HTTP MCP server is unreachable, httpx transport errors must
+complete the pending JSON-RPC waiter instead of escaping into the outer task
+group (which surfaces as an uncatchable cancel-scope RuntimeError).
+"""
+
+from __future__ import annotations
+
+import anyio
+import pytest
+from mcp_types import INTERNAL_ERROR
+
+from mcp.client.session_group import ClientSessionGroup, StreamableHttpParameters
+from mcp.shared.exceptions import MCPError
+
+
+@pytest.mark.anyio
+async def test_unreachable_streamable_http_server_raises_catchable_error() -> None:
+    async with ClientSessionGroup() as group:
+        server_params = StreamableHttpParameters(url="http://127.0.0.1:1/mcp/")
+        with anyio.fail_after(10):
+            with pytest.raises(MCPError) as exc_info:
+                await group.connect_to_server(server_params)
+
+    assert exc_info.value.code == INTERNAL_ERROR
+    assert "Transport error" in exc_info.value.message