In Multi-Agent System (MAS), developers concentrate on creating design models and evolving them, from higher level models to lower level models, in several steps. Considerable part of MAS implementations is automatically produced from the design models. If a design model contains faults, they are passed to the generated implementations. Practical model validation techniques are required to discover and delete faults in abstract design models. In this paper, we introduce a formal approach for MAS design testing. It specifies a testing process that complements Multi-agent Systems Engineering (MaSE) methodology and strengthens the mutual relationship between UML and MAS. Besides, it defines a structured and comprehensive testing process for engineering software agents at the design level by providing a systematic way of converting the MAS design models to UML design diagram. Then a Petri Net (PN) diagram is generated from the UML models to simulate the behavior of the MAS system. Finally, because Petri Nets (PNs) are formal models, their analysis techniques can be applied to automatic MAS behavioral testing.