Recent years have seen growth in the number of algorithms designed to solve challenging simulation-based nonlinear optimization problems. One such algorithm is the Trust-Region Parallel Direct Search (TRPDS) method developed by Hough and Meza. In this paper, we take advantage of the theoretical properties of TRPDS to make use of approximation models in order to reduce the computational cost of simulation-based optimization. We describe the extension, which we call mTRPDS, and present the results of a case study for two earth penetrator design problems. In the case study, we conduct computational experiments with an array of approximations within the mTRPDS algorithm and compare the numerical results to the original TRPDS algorithm and a trust-region method implemented using the speculative gradient approach described by Byrd, Schnabel, and Shultz. The results suggest new ways to improve the algorithm.