Abstract This paper is devoted to the theoretical investigation of combustion of porous media. For the first time the process of flame spread in a layer of a solid porous material with an external supply of a gaseous oxidizer has been analyzed in terms of a heterogeneous model. The multi-stage character of the process (filtration, sorption, chemical reaction) is taken into account. In many practically important cases (e.g., in the case of combustion of coarsely divided particles with the formation of compact films of a condensed product) the sorption stage plays the dominant role in the mechanism of thermal flame spread. This role is developed from a detailed analysis of heat and mass transfer in the model structure of a heterogeneous medium. Such an approach makes it possible to determine explicitly the dependence or the rate of combustion on both the filtration and sorption and structural characteristics of the solid phase (the solubility of gas in the solid phase, the diffusion activation energy, the sizes of pores and particles, etc.).