Although structural testing techniques are among the weakest available with regard to developing confidence in sequential programs, they are not without merit. This paper extends the notion of structural testing criteria to concurrent programs and proposes a hierarchy of supporting structural testing techniques. Coverage criteria described include concurrency state coverage, state transition coverage, and synchronization coverage. Requisite support tools include a static concurrency analyzer and either a program transformation system or a powerful run-time monitor. Also helpful is a controllable run-time scheduler. The techniques proposed are suitable for Ada or CSP-like languages. Best results are obtained for programs having only static naming of tasking objects.