Test data sets have been automatically generated for both numerical and string data types to test the functionality of simple procedures and a good sized UNIX filing system from their Z specifications. Different structured properties of software systems are covered, such as arithmetic expressions, existential and universal quantifiers, set comprehension, union, intersection and difference, etc. A CASE tool ZTEST has been implemented to automatically generate test data sets. Test cases can be derived from the functionality of the Z specifications automatically. The test data sets generated from the test cases check the behaviour of the software systems for both valid and invalid inputs. Test cases are generated for the four boundary values and an intermediate value of the input search domain. For integer input variables, high quality test data sets can be generated on the search domain boundary and on each side of the boundary for both valid and invalid tests. Adaptive methods such as Genetic Algorithms and Simulated Annealing are used to generate test data sets from the test cases. GA is chosen as the default test data generator of ZTEST. Direct assignment is used if it is possible to make ZTEST system more efficient. Z is a formal language that can be used to precisely describe the functionality of computer systems. Therefore, the test data generation method can be used widely for test data generation of software systems. It will be very useful to the systems developed from Z specifications.