Automatic test data generation helps testers to validate software against user requirements more easily. Test data can be generated from many sources; for example, experience of testers, source program, or software specification. Selecting a proper test data set is a decision making task. Testers have to decide what test data that they should use, and a heuristic technique is needed to solve this problem automatically. In this paper, we propose a framework for generating test data from software specifications. The selected specification is Unified Modeling Language (UML) state machine diagram. UML state machine diagram describes a system in term of state which can be changed when there is an action occurring in the system. The generated test data is a sequence of these actions. These sequences of action help testers to know how they should test the system. The quality of generated test data is measured by the number of transitions which is fired using the test data. The more transitions test data can fire, the better quality of test data is. The number of coverage transitions is also used as a feedback for a heuristic search for a better test set. Genetic algorithms (GAs) are selected for searching the best test data. Our experimental results show that the proposed GA-based approach can work well for generating test data for some types of UML state machine diagrams. Keywords- Test data generation, UML state machine diagram, Genetic algorithm.