The one-dimensional flame analysis was carried out to understand the combustion phenomena in porous media. The downstream as well as upstream solution corresponding to upper and lower solutions could be obtained. While upper flame temperature gets higher, lower flame temperature gets lower, as the flame approaches the central part of the combustor. The reason why upstream flame and downstream flame exist at the same flow condition is that the regions where net heat recirculation is identical exist in upstream and downstream of the combustor. In order for the downstream flame to be stabilized, more heats needed to be recirculated towards upstream because of larger radiation loss of downstream flame.