diff --git a/src/mcp/shared/session.py b/src/mcp/shared/session.py
index 90ad92e33..11daedc98 100644
--- a/src/mcp/shared/session.py
+++ b/src/mcp/shared/session.py
@@ -187,7 +187,6 @@ def __init__(
         self._receive_notification_type = receive_notification_type
         self._session_read_timeout_seconds = read_timeout_seconds
         self._in_flight = {}
-
         self._exit_stack = AsyncExitStack()
 
     async def __aenter__(self) -> Self:
@@ -232,45 +231,48 @@ async def send_request(
         ](1)
         self._response_streams[request_id] = response_stream
 
-        self._exit_stack.push_async_callback(lambda: response_stream.aclose())
-        self._exit_stack.push_async_callback(lambda: response_stream_reader.aclose())
-
-        jsonrpc_request = JSONRPCRequest(
-            jsonrpc="2.0",
-            id=request_id,
-            **request.model_dump(by_alias=True, mode="json", exclude_none=True),
-        )
-
-        # TODO: Support progress callbacks
-
-        await self._write_stream.send(JSONRPCMessage(jsonrpc_request))
-
-        # request read timeout takes precedence over session read timeout
-        timeout = None
-        if request_read_timeout_seconds is not None:
-            timeout = request_read_timeout_seconds.total_seconds()
-        elif self._session_read_timeout_seconds is not None:
-            timeout = self._session_read_timeout_seconds.total_seconds()
-
         try:
-            with anyio.fail_after(timeout):
-                response_or_error = await response_stream_reader.receive()
-        except TimeoutError:
-            raise McpError(
-                ErrorData(
-                    code=httpx.codes.REQUEST_TIMEOUT,
-                    message=(
-                        f"Timed out while waiting for response to "
-                        f"{request.__class__.__name__}. Waited "
-                        f"{timeout} seconds."
-                    ),
-                )
+            jsonrpc_request = JSONRPCRequest(
+                jsonrpc="2.0",
+                id=request_id,
+                **request.model_dump(by_alias=True, mode="json", exclude_none=True),
             )
 
-        if isinstance(response_or_error, JSONRPCError):
-            raise McpError(response_or_error.error)
-        else:
-            return result_type.model_validate(response_or_error.result)
+            # TODO: Support progress callbacks
+
+            await self._write_stream.send(JSONRPCMessage(jsonrpc_request))
+
+            # request read timeout takes precedence over session read timeout
+            timeout = None
+            if request_read_timeout_seconds is not None:
+                timeout = request_read_timeout_seconds.total_seconds()
+            elif self._session_read_timeout_seconds is not None:
+                timeout = self._session_read_timeout_seconds.total_seconds()
+
+            try:
+                with anyio.fail_after(timeout):
+                    response_or_error = await response_stream_reader.receive()
+            except TimeoutError:
+                raise McpError(
+                    ErrorData(
+                        code=httpx.codes.REQUEST_TIMEOUT,
+                        message=(
+                            f"Timed out while waiting for response to "
+                            f"{request.__class__.__name__}. Waited "
+                            f"{timeout} seconds."
+                        ),
+                    )
+                )
+
+            if isinstance(response_or_error, JSONRPCError):
+                raise McpError(response_or_error.error)
+            else:
+                return result_type.model_validate(response_or_error.result)
+
+        finally:
+            self._response_streams.pop(request_id, None)
+            await response_stream.aclose()
+            await response_stream_reader.aclose()
 
     async def send_notification(self, notification: SendNotificationT) -> None:
         """
diff --git a/tests/client/test_resource_cleanup.py b/tests/client/test_resource_cleanup.py
new file mode 100644
index 000000000..990b3a89a
--- /dev/null
+++ b/tests/client/test_resource_cleanup.py
@@ -0,0 +1,68 @@
+from unittest.mock import patch
+
+import anyio
+import pytest
+
+from mcp.shared.session import BaseSession
+from mcp.types import (
+    ClientRequest,
+    EmptyResult,
+    PingRequest,
+)
+
+
+@pytest.mark.anyio
+async def test_send_request_stream_cleanup():
+    """
+    Test that send_request properly cleans up streams when an exception occurs.
+
+    This test mocks out most of the session functionality to focus on stream cleanup.
+    """
+
+    # Create a mock session with the minimal required functionality
+    class TestSession(BaseSession):
+        async def _send_response(self, request_id, response):
+            pass
+
+    # Create streams
+    write_stream_send, write_stream_receive = anyio.create_memory_object_stream(1)
+    read_stream_send, read_stream_receive = anyio.create_memory_object_stream(1)
+
+    # Create the session
+    session = TestSession(
+        read_stream_receive,
+        write_stream_send,
+        object,  # Request type doesn't matter for this test
+        object,  # Notification type doesn't matter for this test
+    )
+
+    # Create a test request
+    request = ClientRequest(
+        PingRequest(
+            method="ping",
+        )
+    )
+
+    # Patch the _write_stream.send method to raise an exception
+    async def mock_send(*args, **kwargs):
+        raise RuntimeError("Simulated network error")
+
+    # Record the response streams before the test
+    initial_stream_count = len(session._response_streams)
+
+    # Run the test with the patched method
+    with patch.object(session._write_stream, "send", mock_send):
+        with pytest.raises(RuntimeError):
+            await session.send_request(request, EmptyResult)
+
+    # Verify that no response streams were leaked
+    assert len(session._response_streams) == initial_stream_count, (
+        f"Expected {initial_stream_count} response streams after request, "
+        f"but found {len(session._response_streams)}"
+    )
+
+    # Clean up
+    await write_stream_send.aclose()
+    await write_stream_receive.aclose()
+    await read_stream_send.aclose()
+    await read_stream_receive.aclose()