diff --git a/.changeset/graceful-get-sse-404-406.md b/.changeset/graceful-get-sse-404-406.md
new file mode 100644
index 000000000..75425eec6
--- /dev/null
+++ b/.changeset/graceful-get-sse-404-406.md
@@ -0,0 +1,5 @@
+---
+'@modelcontextprotocol/client': patch
+---
+
+Handle 404 and 406 responses gracefully in GET SSE stream initialization, matching existing 405 behavior. Servers that lack a GET handler (404) or reject `Accept: text/event-stream` (406) now fall back to POST-only communication instead of throwing a fatal error.
diff --git a/packages/client/src/client/streamableHttp.ts b/packages/client/src/client/streamableHttp.ts
index 3d45b60e9..4f1d9bd28 100644
--- a/packages/client/src/client/streamableHttp.ts
+++ b/packages/client/src/client/streamableHttp.ts
@@ -246,9 +246,12 @@ export class StreamableHTTPClientTransport implements Transport {
 
                 await response.text?.().catch(() => {});
 
-                // 405 indicates that the server does not offer an SSE stream at GET endpoint
-                // This is an expected case that should not trigger an error
-                if (response.status === 405) {
+                // These status codes indicate that the server does not offer an SSE stream at the GET endpoint.
+                // 404: server has no GET handler at this endpoint (only POST)
+                // 405: server explicitly rejects GET method
+                // 406: server rejects the Accept header for GET (e.g., does not serve text/event-stream)
+                // All are expected cases that should not trigger an error — the client falls back to POST.
+                if (response.status === 404 || response.status === 405 || response.status === 406) {
                     return;
                 }
 
diff --git a/packages/client/test/client/streamableHttp.test.ts b/packages/client/test/client/streamableHttp.test.ts
index 55bf79a50..d61328b1c 100644
--- a/packages/client/test/client/streamableHttp.test.ts
+++ b/packages/client/test/client/streamableHttp.test.ts
@@ -309,6 +309,64 @@ describe('StreamableHTTPClientTransport', () => {
         expect(globalThis.fetch).toHaveBeenCalledTimes(2);
     });
 
+    it('should handle 404 gracefully when server has no GET handler', async () => {
+        // Mock the server having no GET handler at this endpoint (only POST)
+        (globalThis.fetch as Mock).mockResolvedValueOnce({
+            ok: false,
+            status: 404,
+            statusText: 'Not Found'
+        });
+
+        await transport.start();
+        await expect(transport['_startOrAuthSse']({})).resolves.not.toThrow();
+        expect(globalThis.fetch).toHaveBeenCalledWith(
+            expect.anything(),
+            expect.objectContaining({
+                method: 'GET',
+                headers: expect.any(Headers)
+            })
+        );
+
+        // Verify transport still works after 404
+        (globalThis.fetch as Mock).mockResolvedValueOnce({
+            ok: true,
+            status: 202,
+            headers: new Headers()
+        });
+
+        await transport.send({ jsonrpc: '2.0', method: 'test', params: {} } as JSONRPCMessage);
+        expect(globalThis.fetch).toHaveBeenCalledTimes(2);
+    });
+
+    it('should handle 406 gracefully when server rejects Accept header for GET', async () => {
+        // Mock the server rejecting the Accept: text/event-stream header
+        (globalThis.fetch as Mock).mockResolvedValueOnce({
+            ok: false,
+            status: 406,
+            statusText: 'Not Acceptable'
+        });
+
+        await transport.start();
+        await expect(transport['_startOrAuthSse']({})).resolves.not.toThrow();
+        expect(globalThis.fetch).toHaveBeenCalledWith(
+            expect.anything(),
+            expect.objectContaining({
+                method: 'GET',
+                headers: expect.any(Headers)
+            })
+        );
+
+        // Verify transport still works after 406
+        (globalThis.fetch as Mock).mockResolvedValueOnce({
+            ok: true,
+            status: 202,
+            headers: new Headers()
+        });
+
+        await transport.send({ jsonrpc: '2.0', method: 'test', params: {} } as JSONRPCMessage);
+        expect(globalThis.fetch).toHaveBeenCalledTimes(2);
+    });
+
     it('should handle successful initial GET connection for SSE', async () => {
         // Set up readable stream for SSE events
         const encoder = new TextEncoder();