Feasibility determination has emerged as a widely applied problem in simulation optimization. It seeks to provide all the feasible designs from a finite set of design alternatives based on which the final decision can be chosen by the decision maker. In this paper, we consider the feasibility determination problem in presence of multiple performance measure constraints. The optimal solution to maximize the probability of correct feasibility determination is derived under asymptotic approximation. A corresponding sequential selection procedure is designed for implementation. The numerical testing shows that our approach can enhance the simulation efficiency significantly.