diff --git a/kotlin-sdk-client/src/commonMain/kotlin/io/modelcontextprotocol/kotlin/sdk/client/Client.kt b/kotlin-sdk-client/src/commonMain/kotlin/io/modelcontextprotocol/kotlin/sdk/client/Client.kt
index c86cad83..d861bd08 100644
--- a/kotlin-sdk-client/src/commonMain/kotlin/io/modelcontextprotocol/kotlin/sdk/client/Client.kt
+++ b/kotlin-sdk-client/src/commonMain/kotlin/io/modelcontextprotocol/kotlin/sdk/client/Client.kt
@@ -34,6 +34,7 @@ import io.modelcontextprotocol.kotlin.sdk.types.ListRootsResult
 import io.modelcontextprotocol.kotlin.sdk.types.ListToolsRequest
 import io.modelcontextprotocol.kotlin.sdk.types.ListToolsResult
 import io.modelcontextprotocol.kotlin.sdk.types.LoggingLevel
+import io.modelcontextprotocol.kotlin.sdk.types.McpException
 import io.modelcontextprotocol.kotlin.sdk.types.Method
 import io.modelcontextprotocol.kotlin.sdk.types.PingRequest
 import io.modelcontextprotocol.kotlin.sdk.types.ReadResourceRequest
@@ -54,6 +55,7 @@ import kotlinx.atomicfu.update
 import kotlinx.collections.immutable.minus
 import kotlinx.collections.immutable.persistentMapOf
 import kotlinx.collections.immutable.toPersistentSet
+import kotlinx.serialization.SerializationException
 import kotlinx.serialization.json.JsonObject
 import kotlin.coroutines.cancellation.CancellationException
 
@@ -196,11 +198,15 @@ public open class Client(private val clientInfo: Implementation, options: Client
             logger.error(error) { "Failed to initialize client: ${error.message}" }
             close()
 
-            if (error !is CancellationException) {
-                throw IllegalStateException("Error connecting to transport: ${error.message}", error)
-            }
+            when (error) {
+                is CancellationException,
+                is McpException,
+                is StreamableHttpError,
+                is SerializationException,
+                -> throw error
 
-            throw error
+                else -> throw IllegalStateException("Error connecting to transport: ${error.message}", error)
+            }
         }
     }
 
diff --git a/kotlin-sdk-test/src/commonTest/kotlin/io/modelcontextprotocol/kotlin/sdk/client/ClientTest.kt b/kotlin-sdk-test/src/commonTest/kotlin/io/modelcontextprotocol/kotlin/sdk/client/ClientTest.kt
index d863e008..b4fbcb70 100644
--- a/kotlin-sdk-test/src/commonTest/kotlin/io/modelcontextprotocol/kotlin/sdk/client/ClientTest.kt
+++ b/kotlin-sdk-test/src/commonTest/kotlin/io/modelcontextprotocol/kotlin/sdk/client/ClientTest.kt
@@ -26,6 +26,7 @@ import io.modelcontextprotocol.kotlin.sdk.types.ListToolsResult
 import io.modelcontextprotocol.kotlin.sdk.types.LoggingLevel
 import io.modelcontextprotocol.kotlin.sdk.types.LoggingMessageNotification
 import io.modelcontextprotocol.kotlin.sdk.types.LoggingMessageNotificationParams
+import io.modelcontextprotocol.kotlin.sdk.types.McpException
 import io.modelcontextprotocol.kotlin.sdk.types.Method
 import io.modelcontextprotocol.kotlin.sdk.types.Role
 import io.modelcontextprotocol.kotlin.sdk.types.Root
@@ -232,6 +233,82 @@ class ClientTest {
         assertTrue(closed)
     }
 
+    @Test
+    fun `should rethrow McpException as is`() = runTest {
+        var closed = false
+        val failingTransport = object : AbstractTransport() {
+            override suspend fun start() {}
+
+            override suspend fun send(message: JSONRPCMessage) {
+                if (message !is JSONRPCRequest) return
+                check(message.method == Method.Defined.Initialize.value)
+                throw McpException(
+                    code = -32600,
+                    message = "Invalid Request",
+                )
+            }
+
+            override suspend fun close() {
+                closed = true
+            }
+        }
+
+        val client = Client(
+            clientInfo = Implementation(
+                name = "test client",
+                version = "1.0",
+            ),
+            options = ClientOptions(),
+        )
+
+        val exception = assertFailsWith<McpException> {
+            client.connect(failingTransport)
+        }
+
+        assertEquals(-32600, exception.code)
+        assertEquals("MCP error -32600: Invalid Request", exception.message)
+
+        assertTrue(closed)
+    }
+
+    @Test
+    fun `should rethrow StreamableHttpError as is`() = runTest {
+        var closed = false
+        val failingTransport = object : AbstractTransport() {
+            override suspend fun start() {}
+
+            override suspend fun send(message: JSONRPCMessage) {
+                if (message !is JSONRPCRequest) return
+                check(message.method == Method.Defined.Initialize.value)
+                throw StreamableHttpError(
+                    code = 500,
+                    message = "Internal Server Error",
+                )
+            }
+
+            override suspend fun close() {
+                closed = true
+            }
+        }
+
+        val client = Client(
+            clientInfo = Implementation(
+                name = "test client",
+                version = "1.0",
+            ),
+            options = ClientOptions(),
+        )
+
+        val exception = assertFailsWith<StreamableHttpError> {
+            client.connect(failingTransport)
+        }
+
+        assertEquals(500, exception.code)
+        assertEquals("Streamable HTTP error: Internal Server Error", exception.message)
+
+        assertTrue(closed)
+    }
+
     @Test
     fun `should respect server capabilities`() = runTest {
         val serverOptions = ServerOptions(
@@ -922,7 +999,7 @@ class ClientTest {
                 println("Client connected")
             },
             launch {
-                serverSessionResult.complete(server.connect(serverTransport))
+                serverSessionResult.complete(server.createSession(serverTransport))
                 println("Server connected")
             },
         ).joinAll()