The flame sheet approximation (FS) and a novel polynomial approximation technique (PA) are compared in terms of their capability to describe reaction fronts of highly exothermic reactions in a porous medium. A one-phase model and a two-phase model of a system with adiabatic walls and a radiant output (to approximate the case of a porous radiant burner) are included in the analysis. By matching the reaction zone solution found by either the FS or PA method with the solutions of the nonreacting zones, the temperature, conversion, and position of the reaction zone were determined. Numerical solutions for catalytic and noncatalytic oxidation reactions were used to compare the predictions of both approaches. It was found that although both techniques yielded good approximations to the solutions, the PA technique proved to be more accurate, producing results with 3.5% of the numerical results. Both methods can find useful application in the analysis of this class of problems.