This research considers the problem of ranking the top simulated designs in the presence of stochastic constraints. The objective and constraint measures of each design must be estimated via simulation. Given a fixed simulation budget, the ranking of the top feasible designs cannot be determined with certainty. The objective of this research is to derive an efficient simulation budget allocation strategy such that the probability of correct ranking (PCR) can be maximized. To deal with this problem, we propose a lower bound on the PCR and develop an asymptotically optimal allocation rule based on the lower bound. Useful insights on characterizing the allocation rule are provided, and numerical experiments are carried out to demonstrate the efficiency of the suggested simulation procedure. (C) 2019 Elsevier Ltd. All rights reserved.