By developing our proper CFD code under Fortran, the performances of a Stirling engine are studied in unsteady laminar regime and closely linked to the properties of its regenerator. However, it is responsible about the maximum part of losses in the Stirling engine. These losses depend on geometric and physical properties of the material constituting the regenerator. Thus, finding the suitable regenerator material that generates the greatest heat exchange and the lowest pressure drop is a good solution to reduce sources of irreversibility and ameliorate the global performances of the Stirling engine. The aim of this paper is to describe oxillatory flow and heat transfer inside porous regenerator materials and to determine the most suitable regenerator material. Brinkman-Forchheimer-Lapwood extended Darcy model is assumed to simulate momentum transfer within the porous regenerator. And the oscillatory flow is described by the Navier-Stockes compressible equations. The local thermal equilibrium of the gas and the matrix is taken into account for the modelling of the porous regenerator. The governing equations with the appropriate boundary conditions are solved by the control volume based finite element method (CVFEM). A numerical code on the software Fortran is elaborated to evaluate flow and heat transfer characteristics inside regenerator. Results showed that the fluid flow and heat transfer between the compression and expansion phases were varied significantly. It was shown that the superior comprehensive performance of the regenerator makes it possible to improve the performance of Stirling engines.