Heat Transfer with ablation in a two-dimensional region subjected to time variant heat fluxes at boundary is studied. A modified heat balance integral method is employed. Using a double integral in space and assuming a linear profile for the ablating front, the complicated second order partial differential equation is reduced to a system of ordinary differential equations. Reasonably good agreement between the present solution and a finite element solution is found. Emphasis of this study is placed on the evaluation of the total material loss as function of time rather than the determination of temperature profile itself.