variavel0=Daniela V. F. M. Rey Silva - daniela@lttc.coppe.ufrj.br COPPE/UFRJ Helcio R. B. Orlande - helcio@serv.com.ufrj.br COPPE/UFRJ Abstract. This paper deals with the numerical solution of the heat transfer problem in materials typically utilized for the thermal protection of space vehicles. The solution methodology implemented is specially important for the design of thermal protection systems for space vehicles subjected to extremely high heat loads, such as those undergoing atmospheric reentry. We solve here the one-dimensional problem in an ablating material. Thermal decomposition of the material is taken into account. The numerical solution for the problem is obtained with the finite-volume method. Results are presented for a thermal protection material with thermophysical properties found in the literature. Keywords. ablation, thermal protection system, atmospheric reentry, enthalpy formulation, finite-volume.