A mathematical model of thermal decomposition together with the flammability limit is proposed to describe the pyrolysis and spontaneous ignition of wood slab subjected to the radiation from a truncated-cone heater. The prominent physical and chemical phenomena were considered in the model, involving heat transfer in a solid, heat consumed by thermal decomposition reactions, the evaporation of moisture, re-radiation from pore surfaces inside a solid and so on. The numerical solution allows the prediction of in-depth temperature profiles, evolution of volatiles, variation of thermal conductivity, apparent mass loss (solid conversion) and ignition time. The different densities for wood species and effect of moisture content and grain orientation on thermal conductivity are also considered in the model, producing a good prediction of surface temperatures. This gives birth to the reasonable prediction on ignition time of wood by employing fixed surface temperature (400 ℃) as ignition criterion. However, the analysis of constituent fractions for the species associated with the multi-components kinetic scheme should be included in the mathematical model to give a more precise prediction on the apparent mass loss of solid.