 The goal of the paper is the numerical study of the original hysteresis computational material models and their application in beams bending theory. The paper presents the chosen differential material models and approaches based on step-by-step solution respecting the elastic and plastic conditions. In the center of author's interest is the numerical method study of the plastic zones identification or study of residual stresses distribution in the beams cross-section. The results obtained from new MATLAB's programs are compared with FEM models in Adina. This article was authored by Milan Saga, Milan Vasco, Peter Kopis, and others.