We consider a mathematical model of thermal degradation of thick solids which is formulated in terms of a general kinetic rate law. The model is applicable to many fire-test situations, notably the standard cone calorimeter test where a horizontal sample is exposed to a uniform heat Bur. The model incorporates a mechanism for the transfer of mass through the material as vaporisation occurs - a feature neglected in many mathematical models published to date. Attention is focused on a single-step nth. order Arrhenius reaction for the thermal degradation. Results are presented which quantify the effects of incident heat flux, hear losses and kinetic mechanism on the temperature distribution in the solid and the mass loss rate. In particular we demonstrate that thermal history strongly affects mass loss rate for materials that degrade according to reactions of non-unitary order. The consequences of this and other effects on the ignition characteristics of solids are briefly discussed.