A two-dimensional, unsteady, nonconstant property mathematical model of the degradation of porous cellulosic fuels to volatiles and chars, including convective and conductive heat transfer, is coupled to a quasi-steady, two-dimensional mathematical model, including gas phase momentum, energy and chemical species mass equations, to simulate downward flame spread. Three main regimes of flame spread are established as the fuel thickness is varied. The first, where the spread rate increases with the solid thickness, is observed for a narrow range of very thin solids and is controlled by gas-phase chemical kinetics. In the second regime, the spread rates, which compare favorably with experimental measurements, decrease as the solid thickness is increased (thermally thin regime). Finally, as the fuel thickness is increased beyond a certain limit, the thermally thick regime, that is a constant spread rate, is simulated. Good agreement between the spread rates predicted by the numerical model and the analytical theory by de Ris is obtained in the limit of the thermally thin and thermally thick regime. However, the transition from one regime to the other occurs for largely different fuel thicknesses. The mechanisms of energy feedback to the unburned solid ahead of the flame have also been investigated. Gas-phase heat conduction dominates the first and the second regime of flame spread. The contribution of solid-phase heat conduction to the energy transfer ahead of the flame increases with the fuel thickness reaching, for thermally thick solids, a maximum of about 50% of the total energy transferred.