The thermal response analysis of an ablative material on a two dimensional external surface is performed. The method considers the whole domain as one continuous computational domain, eliminating the necessity to check the starting and ending positions of the decomposition zone. The current study solves the decomposition of the material at high temperatures by using the nth order Arrhenius equation but excludes the removal of char from the surface due to mechanical erosion or phase change and considers that the ablation process takes place in a finite zone. Pyrolysis gases are assumed to behave as ideal gas and the pressure Is taken as a constant on the whole physical domain. The formulation for one-dimensional case is validated by experimental results obtained from literature. The two-dimensional case in a Cartesian geometry is formulated and an algebraic transformation is used to normalize the region in both directions and transform at same time into a square computational domain in order to get a solution for variable thickness domains. The formulation for two-dimensional case is revised for the cylindrical coordinates with a finite length in the axial direction. To solve geometries where the outer surface deviates from cylindrical, the formulation is scaled and transformed into a non-dimensional square computational domain. In all problems, the radiation, constant heat flux and adiabatic wall boundary conditions exist and the entire domain is initially at a constant temperature.