diff --git a/google-cloud-spanner/src/main/java/com/google/cloud/spanner/SessionPool.java b/google-cloud-spanner/src/main/java/com/google/cloud/spanner/SessionPool.java
index c4751d159b3..e9011d0ff83 100644
--- a/google-cloud-spanner/src/main/java/com/google/cloud/spanner/SessionPool.java
+++ b/google-cloud-spanner/src/main/java/com/google/cloud/spanner/SessionPool.java
@@ -2251,12 +2251,15 @@ private PooledSession pollUninterruptiblyWithTimeout(
             interrupted = true;
           } catch (TimeoutException e) {
             if (acquireSessionTimeout != null) {
-              throw SpannerExceptionFactory.newSpannerException(
-                  ErrorCode.RESOURCE_EXHAUSTED,
-                  "Timed out after waiting "
-                      + acquireSessionTimeout.toMillis()
-                      + "ms for acquiring session. To mitigate error SessionPoolOptions#setAcquireSessionTimeout(Duration) to set a higher timeout"
-                      + " or increase the number of sessions in the session pool.");
+              SpannerException exception =
+                  SpannerExceptionFactory.newSpannerException(
+                      ErrorCode.RESOURCE_EXHAUSTED,
+                      "Timed out after waiting "
+                          + acquireSessionTimeout.toMillis()
+                          + "ms for acquiring session. To mitigate error SessionPoolOptions#setAcquireSessionTimeout(Duration) to set a higher timeout"
+                          + " or increase the number of sessions in the session pool.");
+              waiter.setException(exception);
+              throw exception;
             }
             return null;
           } catch (ExecutionException e) {
diff --git a/google-cloud-spanner/src/test/java/com/google/cloud/spanner/SpanExceptionTest.java b/google-cloud-spanner/src/test/java/com/google/cloud/spanner/SpanExceptionTest.java
new file mode 100644
index 00000000000..2f16cd7c922
--- /dev/null
+++ b/google-cloud-spanner/src/test/java/com/google/cloud/spanner/SpanExceptionTest.java
@@ -0,0 +1,88 @@
+/*
+ * Copyright 2024 Google LLC
+ *
+ * Licensed under the Apache License, Version 2.0 (the "License");
+ * you may not use this file except in compliance with the License.
+ * You may obtain a copy of the License at
+ *
+ *       http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ */
+
+package com.google.cloud.spanner;
+
+import static org.junit.Assert.assertNull;
+import static org.junit.Assert.assertTrue;
+
+import com.google.cloud.NoCredentials;
+import com.google.cloud.spanner.connection.AbstractMockServerTest;
+import io.grpc.ManagedChannelBuilder;
+import java.util.ArrayList;
+import java.util.concurrent.ExecutionException;
+import java.util.concurrent.ExecutorService;
+import java.util.concurrent.Executors;
+import java.util.concurrent.Future;
+import java.util.concurrent.TimeUnit;
+import org.junit.Test;
+import org.junit.runner.RunWith;
+import org.junit.runners.JUnit4;
+import org.threeten.bp.Duration;
+
+@RunWith(JUnit4.class)
+public class SpanExceptionTest extends AbstractMockServerTest {
+
+  @Test
+  public void testReadOnlyTransaction() throws InterruptedException, ExecutionException {
+    try (Spanner spanner =
+        SpannerOptions.newBuilder()
+            .setProjectId("my-project")
+            .setHost(String.format("http://localhost:%d", getPort()))
+            .setChannelConfigurator(ManagedChannelBuilder::usePlaintext)
+            .setCredentials(NoCredentials.getInstance())
+            .setSessionPoolOption(
+                SessionPoolOptions.newBuilder()
+                    .setMaxSessions(10)
+                    .setAcquireSessionTimeout(Duration.ofMillis(10))
+                    // .setAcquireSessionTimeout(null)
+                    .build())
+            .build()
+            .getService()) {
+      DatabaseClient client = spanner.getDatabaseClient(DatabaseId.of("p", "i", "d"));
+
+      int numThreads = 25;
+      ExecutorService service = Executors.newFixedThreadPool(numThreads);
+      ArrayList<Future<Void>> futures = new ArrayList<>(numThreads);
+      try (ReadOnlyTransaction readOnlyTransaction = client.readOnlyTransaction()) {
+        for (int i = 0; i < numThreads; i++) {
+          futures.add(service.submit(() -> executeRandom(readOnlyTransaction)));
+        }
+        service.shutdown();
+        assertTrue(service.awaitTermination(60L, TimeUnit.SECONDS));
+        // Verify that all threads finished without any unexpected errors.
+        for (Future<Void> future : futures) {
+          assertNull(future.get());
+        }
+      }
+    }
+  }
+
+  private Void executeRandom(ReadOnlyTransaction readOnlyTransaction) {
+    try (ResultSet resultSet = readOnlyTransaction.executeQuery(SELECT_RANDOM_STATEMENT)) {
+      while (resultSet.next()) {
+        // ignore
+      }
+    } catch (SpannerException spannerException) {
+      if (spannerException.getErrorCode() == ErrorCode.RESOURCE_EXHAUSTED) {
+        // This is the expected error code, so ignore.
+        return null;
+      }
+      throw spannerException;
+    }
+    return null;
+  }
+}