In the present study, numerical simulations for smoldering in a horizontal channel are performed for both compressible and incompressible flows. The reactant gas is passing through the char surface, where the chemical reaction is going to take place. For the sake of simplicity, the smoldering is treated to be a single step chemical reaction. In the incompressible flow, a set of governing parameters are discussed to elucidate their influences on the process of smoldering. Furthermore, the variations of density and dynamic viscosity of gaseous mixture are taken into account in the compressible flow. The comparison between the compressible and incompressible flows reveals that the effects of local compressibility and gaseous mixture on the propagation of smoldering wave are striking.