diff --git a/.git-blame-ignore-revs b/.git-blame-ignore-revs
new file mode 100644
index 00000000..e69de29b
diff --git a/.gitignore b/.gitignore
index bb25f9e4..54006f93 100644
--- a/.gitignore
+++ b/.gitignore
@@ -1,4 +1,5 @@
 .DS_Store
+scratch/
 
 # Byte-compiled / optimized / DLL files
 __pycache__/
diff --git a/src/mcp/server/lowlevel/server.py b/src/mcp/server/lowlevel/server.py
index 643e1a27..c0008b32 100644
--- a/src/mcp/server/lowlevel/server.py
+++ b/src/mcp/server/lowlevel/server.py
@@ -68,9 +68,10 @@ async def main():
 import logging
 import warnings
 from collections.abc import Awaitable, Callable
-from contextlib import AbstractAsyncContextManager, asynccontextmanager
+from contextlib import AbstractAsyncContextManager, AsyncExitStack, asynccontextmanager
 from typing import Any, AsyncIterator, Generic, Sequence, TypeVar
 
+import anyio
 from anyio.streams.memory import MemoryObjectReceiveStream, MemoryObjectSendStream
 from pydantic import AnyUrl
 
@@ -469,41 +470,47 @@ async def run(
         # in-process servers.
         raise_exceptions: bool = False,
     ):
-        with warnings.catch_warnings(record=True) as w:
-            from contextlib import AsyncExitStack
-
-            async with AsyncExitStack() as stack:
-                lifespan_context = await stack.enter_async_context(self.lifespan(self))
-                session = await stack.enter_async_context(
-                    ServerSession(read_stream, write_stream, initialization_options)
-                )
+        async with AsyncExitStack() as stack:
+            lifespan_context = await stack.enter_async_context(self.lifespan(self))
+            session = await stack.enter_async_context(
+                ServerSession(read_stream, write_stream, initialization_options)
+            )
 
+            async with anyio.create_task_group() as tg:
                 async for message in session.incoming_messages:
                     logger.debug(f"Received message: {message}")
 
-                    match message:
-                        case (
-                            RequestResponder(
-                                request=types.ClientRequest(root=req)
-                            ) as responder
-                        ):
-                            with responder:
-                                await self._handle_request(
-                                    message,
-                                    req,
-                                    session,
-                                    lifespan_context,
-                                    raise_exceptions,
-                                )
-                        case types.ClientNotification(root=notify):
-                            await self._handle_notification(notify)
-
-                    for warning in w:
-                        logger.info(
-                            "Warning: %s: %s",
-                            warning.category.__name__,
-                            warning.message,
+                    tg.start_soon(
+                        self._handle_message,
+                        message,
+                        session,
+                        lifespan_context,
+                        raise_exceptions,
+                    )
+
+    async def _handle_message(
+        self,
+        message: RequestResponder[types.ClientRequest, types.ServerResult]
+        | types.ClientNotification
+        | Exception,
+        session: ServerSession,
+        lifespan_context: LifespanResultT,
+        raise_exceptions: bool = False,
+    ):
+        with warnings.catch_warnings(record=True) as w:
+            match message:
+                case (
+                    RequestResponder(request=types.ClientRequest(root=req)) as responder
+                ):
+                    with responder:
+                        await self._handle_request(
+                            message, req, session, lifespan_context, raise_exceptions
                         )
+                case types.ClientNotification(root=notify):
+                    await self._handle_notification(notify)
+
+            for warning in w:
+                logger.info(f"Warning: {warning.category.__name__}: {warning.message}")
 
     async def _handle_request(
         self,
diff --git a/tests/issues/test_188_concurrency.py b/tests/issues/test_188_concurrency.py
new file mode 100644
index 00000000..a56c0d30
--- /dev/null
+++ b/tests/issues/test_188_concurrency.py
@@ -0,0 +1,49 @@
+import anyio
+from pydantic import AnyUrl
+
+from mcp.server.fastmcp import FastMCP
+from mcp.shared.memory import (
+    create_connected_server_and_client_session as create_session,
+)
+
+_sleep_time_seconds = 0.01
+_resource_name = "slow://slow_resource"
+
+
+async def test_messages_are_executed_concurrently():
+    server = FastMCP("test")
+
+    @server.tool("sleep")
+    async def sleep_tool():
+        await anyio.sleep(_sleep_time_seconds)
+        return "done"
+
+    @server.resource(_resource_name)
+    async def slow_resource():
+        await anyio.sleep(_sleep_time_seconds)
+        return "slow"
+
+    async with create_session(server._mcp_server) as client_session:
+        start_time = anyio.current_time()
+        async with anyio.create_task_group() as tg:
+            for _ in range(10):
+                tg.start_soon(client_session.call_tool, "sleep")
+                tg.start_soon(client_session.read_resource, AnyUrl(_resource_name))
+
+        end_time = anyio.current_time()
+
+        duration = end_time - start_time
+        assert duration < 3 * _sleep_time_seconds
+        print(duration)
+
+
+def main():
+    anyio.run(test_messages_are_executed_concurrently)
+
+
+if __name__ == "__main__":
+    import logging
+
+    logging.basicConfig(level=logging.DEBUG)
+
+    main()