<p>A new micro-scale refrigeration system composed of arrays of silicon MEMS cooling elements that operate on the Stirling cycle has been designed. In this paper, we describe a multiphysics computational approach for analyzing the system performance that considers compressible flow and heat transfer with a large deformable mesh. The regenerator pressure drop and effectiveness are first explored to determine the optimal porosity. A value near 0.9 is found to maximize the coefficient of performance. To overcome the computational complexity brought about by the fine pillar structure in the regenerator, a porous medium model is used to allow for modeling of a full element. Parametric studies demonstrate the effect of the operating frequency on the cooling capacity and the coefficient of performance.</p