This work presents a numerical study of the stabilization diagram of methane/air premixed flames in a finite porous media foam with a uniform ambient temperature. A set of steady computations are considered, using a I D numerical model that takes into account solid and gas energy equations as well as chemistry and radiation models. The present results show that both stable and unstable solutions, for upper and lower flames, exist either at the surface or submerged in the porous matrix. The influence of the ID computational domain, boundary conditions, and gas/solid interface treatment on the stability of the calculated flames is also discussed. A linearized version of the discrete-ordinates radiation model is included in the linear stability analysis to discuss the influence of radiation on the stability of the flames. The full stabilization diagram and the linear stability analysis provide information on the stability of the flames, pointing to the existence of unstable upstream surface flames as well as unstable submerged flames on the downstream part of the porous media. (c) 2008 The Combustion Institute. Published by Elsevier Inc. All rights reserved.