On the basis of previously published information and new experimental data, presented here, a physical model of subsonic flame propagation in closed vessels with an inert porous medium and combustible gas mixture has been formulated. A mathematical model adequate to describe the physical model has been developed. The model allows the determination of the state of unburned gas and combustion products during the combustion process. Comparison of theoretically predicted and experimental temperature distributions in combustion products shows satisfactory agreement. Interpretation is provided for the specific phenomena observed in the system under study: low end pressure values; dynamic pressure decreasing during the process; anti-h?ache effect; regime transitions accompanied by decreasing flame velocity, and quenching.