The presence of discontinuities in solids causes a stress concentration in their vicinity and a decrease in the durability of solids. In this paper the results of the MATLAB finite element modelling of a square isotropic elastic plane with a central near-elliptical non-smooth hole under uniaxial tension are compared with the analytical solution to the similar problem for an infinite isotropic elastic plane with an elliptical hole. A program for the stress calculation around the hole was developed using the MATLAB code (but not the Toolbox graphical user interface). The aim of this paper was to choose calculation parameters to minimize the difference between the mentioned analytical and MATLAB finite element solutions for further applications.