A 2-D computational model was developed to simulate experiments at the University of Minnesota, UMN, (unsteady heat transfer measurements provided in a companion paper) for a Stirling Engine regenerator matrix. The CFD-ACE+ commercial CFD code was utilized for this study. The model is composed of eight cylinders in cross flow with a staggered arrangement and inlet/outlet plenums. We matched the UMN test section for: the wire diameter, inlet velocity, flow oscillation frequency and matrix porosity. A laminar flow model was utilized in this study and its results were compared with unidirectional flow measurements done at the UMN for the same matrix. Comparison was made, also, for unidirectional heat transfer correlations for porous media available in the literature. Also, we compared our oscillatory heat transfer CFD results with the measurements done at the UMN. The unidirectional results from this study compared well for fluid flow and heat transfer. The oscillatory flow heat transfer results showed phase angle and magnitude differences compared with the UMN data. It is believed that the CFD model although represented the fluid mechanics well, it did not match the UMN thermal boundary conditions.