How to write unit test for "InterruptedException"

Right before invoking addMessage(), call Thread.currentThread().interrupt(). This will set the "interrupt" status flag on the thread.

If the interrupted status is set when the call to put() is made on a LinkedBlockingQueue, an InterruptedException will be raised, even if no waiting is required for the put (the lock is un-contended).

By the way, some efforts to reach 100% coverage are counter-productive and can actually degrade the quality of code.

Use a mocking library like Easymock and inject a mock LinkedBlockingQueue

i.e.

@Test(expected=InterruptedException.class)
public void testInterruptedException() {
    LinkedBlockingQueue queue = EasyMock.createMock(LinkedBlockingQueue.class);
    ExampleMessage message = new ExampleMessage();
    queue.put(message);
    EasyMock.expectLastCall.andThrow(new InterruptedException()); 
    replay(queue);
    someObject.setQueue(queue);
    someObject.addMessage(msg);
}

As stated above just make use Thread.currentThread().interrupt() if you caught InterruptedException and isn't going to rethrow it.

As for the unit testing. Test this way: Assertions.assertThat(Thread.interrupted()).isTrue();. It both checks that the thread was interrupted and clears the interruption flag so that it won't break other test, code coverage or anything below.