Analytical closed-form solution to the stress distribution associated with a hole in finite plates subjected to tension has not been obtained yet. Wherefore, a method developed in this paper is based on a Beltrami-Michell methodology analyzing the Kirsch's problem under finite dimensions conditions of both plane stress and plane strain. This aimed ability is achieved by combining the Beltrami-Michell plane equations, isochromatic information on the boundaries only; and the finite difference method into an effectual hybrid method for analyzing rectangular plates of finite width with circular holes. Furthermore, the Beltrami-Michell methodology suggested may be applied on other plate and cut-out forms.

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This paper is concerned with the "Study of photoelasticity and a photoelastic theoretical investigation of the stress distribution in Square Blocks subjected to concentrated diagonal loads", a thesis topic by M.M. Frocht who developed the well-known semi empirical Shear Stress Difference method. Indeed, the use of the Beltrami-Michell methodology remains quick, when complemented by photoelasticity to acquire Dirichlet's conditions. The synergy of both methods is enhanced with the use of the finite difference method. In addition, a finite element analysis has provided results that will be a supplementary reference for validation. The results obtained have been of lower cost than those obtained by Frocht.