The problem of transient heat transfer in a two-dimensional solid subject to ablation is solved using the equivalent heat capacity method coupled with a finite element approach. To avoid regridding of the system due to disappearance of material, the ablated element is simulated by a fictitious element with zero heat capacity. The numerical result of the ablation front and the material loss as functions of time are presented for various heat fluxes at the boundary. The numerical results are found to compare reasonably well with the approximate solutions of the same problem.