A numerical analysis has been performed extensively with respect to a one dimensional model for radiation controlled flame, where a combustible mixture flows through a porous medium in which the combustion reaction takes place. The comprehensive features revealed in this study may be summarized in the following way: (1) It has shown that a radiation controlled flame is stabilized in a porous medium with extremely high porocity when the combustible gas mixture flows in a porous medium and the structures and burning velocity have been revealed. (2) It has shown that the thermal structures in a porous medium depend strongly on the absorption coefficient and total optical thickness of the porous medium, and their effects on the flame structures and burning velocity have been elucidated. (3) The local and total energy balances of the system have been revealed and the importance of radiation heat loss has been demonstrated.