Presents the design of the software system ADTEST (ADa TESTing), for generating test data for programs developed in Ada83. The key feature of this system is that the problem of test data generation is treated entirely as a numerical optimization problem and, as a consequence, this method does not suffer from the difficulties commonly found in symbolic execution systems, such as those associated with input variable-dependent loops, array references and module calls. Instead, program instrumentation is used to solve a set of path constraints without explicitly knowing their form. The system supports not only the generation of integer and real data types, but also non-numerical discrete types such as characters and enumerated types. The system has been tested on large Ada programs (60,000 lines of code) and found to reduce the effort required to test programs as well as providing an increase in test coverage.