Infiltration-mediated combustion of a thin porous cylinder in reactive gas was studied by mathematical modeling. Gas reagent is infiltrated through an annular gap left of the side surface. In conditions of instability, the self-sustained propagation of individual cellular spots of exothermic combustion was observed. The structure of cellular waves, their dynamics, and travel direction are defined by such factors as temperature profile, pressure gradients, heat release rate, porous structure, and heat losses. Cellular combustion of Ti powder in dish was also explored experimentally and the results were compared with theoretical predictions.