In this article, a two-dimensional axisymmetric cylindrical model for laminar and turbulent combustive reactive flows in porous media is simulated numerically using a finite volume method based on the SIMPLE algorithm. A k-epsilon model is adapted to the porous structure to investigate premixed combustion of methane/air. The numerical results obtained for an operational porous burner show that the turbulent gas temperature stays below the corresponding laminar temperature all over the combustion region, and the length of the reaction zone becomes wider in turbulent flames. Moreover, the effects of changing the thermal and porous structure parameters on the combustion characteristics and the quality of flame stabilization are investigated in detail.