An unsteady one-dimensional model for the solid phase is applied to simulate the spontaneous ignition and burning of thick wood samples with grain orientation parallel or perpendicular to incident heat fluxes in the range 18–40 kW/m2, that is, in the absence of flame. The description of heat and mass transfer processes, at constant gas pressure, is combined with global volumetric rates of wood decomposition and char oxidation. Surface regression occurs for a limit value of char density while a critical surface temperature describes ignition. Good quantitative predictions are obtained for the ignition times and the surface temperature and mass loss rate profiles during burning. Conversion always consists of three main stages. The first short transients correspond to the formation of a relatively thin charred surface layer and glowing ignition. The second much longer stage represents a pseudo-steady-state burning, where the rates of advancement of the decomposition and oxidation zones are approximately constant as well as the surface temperature and the global rate of mass loss. Finally, the last short stage, resulting from the adiabatic bottom condition, is the enlargement of the decomposition zone to the entire sample. The first transient stage and the ignition times are noticeably affected by the external heating conditions whereas the characteristics of the pseudo-steady-state burning are mainly dependent on the char oxidation rate, which is controlled by the oxygen diffusion rate.