Starting with a UML specification that captures the underlying functionality of some given Java-based concurrent system, we describe a systematic way to construct, from this specification, test sequences for validating an implementation of the system. The approach is to first extend the specification to create UML state machines that directly address those aspects of the system we wish to test. To be specific, the extended UML state machines can capture state information about the number of waiting threads or the number of threads blocked on a given object. Using the SAL model checker we can generate from the extended UML state machines sequences that cover all the various possibilities of events and states. These sequences can then be directly transformed into test sequences suitable for input into a testing tool such as ConAn. As an illustration, the methodology is applied to generate sequences for testing a Java implementation of the producer-consumer system.