A method is proposed for the determination of the internal stresses in a two-dimensional system from data furnished by a photoelastic analysis. The method involves the numerical integration of the Laplace and Poisson type difference equations over a region with known boundary values by the iteration of a set of calculus of variations formulas. In this the complete system of internal stresses is computed, using the data obtained from the usual fringe photograph, without recourse to isoclinic lines, or other supplementary experimental measurements. Comparison of the calculated results and those obtained from elasticity shows close agreement.