A finite element approach is employed in the analysis of one-dimensional heat transfer in solids with variable thermal properties and ablating boundary condition. The solid under consideration is subjected to simultaneous thermal radiation, concentrate heat flux and convection. In the analysis, the effect of heat of ablation is approximated by using a large heat capacity over a small temperature range in the vicinity of the melting temperature. To simulate the removal of the melt, fictitious elements with zero capacity and a large conductivity are employed for the ablated material. Consideration has been given to the ablation of a graphite-epoxy composite which is subjected to a uniform heat flux due to laser irradiation; the slab dissipated heat by thermal radiation and forced convection at one side and is insulated at the other side. The present predicted surface recession and the temperature distribution in the unmelted slab are compared with the experimental data and a finite difference solution available in the literature.