diff --git a/src/main/ExceptionHandler.kt b/src/main/ExceptionHandler.kt
index f29bf14..0ce3ec5 100644
--- a/src/main/ExceptionHandler.kt
+++ b/src/main/ExceptionHandler.kt
@@ -28,6 +28,13 @@ class ExceptionHandler {
                 )
             }
 
+            is FullBufferException -> {
+                call.respondText(
+                    "Service is currently unavailable because too many tasks are running.",
+                    status = HttpStatusCode.ServiceUnavailable
+                )
+            }
+
             else -> {
                 call.respondText(
                     "500: $cause. Stack trace: ${cause.stackTraceToString()}",
diff --git a/src/test/TaskManagerTest.kt b/src/test/TaskManagerTest.kt
index e347b0a..f374460 100644
--- a/src/test/TaskManagerTest.kt
+++ b/src/test/TaskManagerTest.kt
@@ -1,8 +1,10 @@
+import com.github.statnett.loadflowservice.FullBufferException
 import com.github.statnett.loadflowservice.Task
 import com.github.statnett.loadflowservice.TaskManager
 import com.github.statnett.loadflowservice.TaskStatus
 import junit.framework.TestCase.*
 import kotlin.test.Test
+import kotlin.test.assertFailsWith
 
 class TaskManagerTest {
     @Test
@@ -31,4 +33,25 @@ class TaskManagerTest {
         assertNull(tm.queue.get(task1.id))
         assertEquals(2, tm.queue.size())
     }
+
+    @Test
+    fun `test tasks not inserted when max number of tasks are running`() {
+        val maxRunning = 5
+        val tm = TaskManager(maxRunning)
+        repeat (maxRunning) { tm.register(runningTask()) }
+        assertEquals(maxRunning, tm.numRunning())
+        assertEquals(maxRunning, tm.size())
+
+        // When inserting one more, it should raise FullBufferError
+        assertFailsWith<FullBufferException> { tm.register(runningTask()) }
+
+        // Verify that the task was not inserted
+        assertEquals(maxRunning, tm.size())
+    }
+}
+
+fun runningTask(): Task {
+    val task = Task()
+    task.status = TaskStatus.RUNNING
+    return task
 }
\ No newline at end of file