A two-dimensional, unsteady, variable property model of the smoldering combustion of an insulating celiulosic bed, in still air, is presented. Chemical processes account for pyrolytic (endothermic)and oxidative (exothermic) degradation of cellulose to volatiles and char, followed by (exothermic) oxidation of char. Physical processes are described by energy, momentum and mass balances for the highly porous solid. The smoldering wave presents a multi-dimensional structure, affected by oxygen transport to the reaction zone (km) and heat losses from the top (hc) and bottom (hw) surfaces of the bed. In particular, as the mass transport coefficient is increased, not only reaction extent but also reaction selectivity varies, with solid pyrolysis becoming more important than solid oxidation. The dependence of the smoldering process on the chemical pathways has also been studied through variations in the pre-exponential factors of the reaction rates.