Based on a mathematical model of a porous reacting medium the statement and mathematical solution are presented for a problem of the peat smoldering rise as a result of the effect of a lower seat of fire. It is found that at moderate temperatures T ≤ 750 K the firing and smoldering of the initial reagent are determined by the intensity of the external burning seat as well as by the processes of the peat drying, pyrolysis, and the oxidation reaction of the coked fixed bed.