The purpose of this article is to present the developed methodology, a brief algorithm of mechanical-and-mathematical modeling to investigate the causes and mechanism of soil disruption from the hillsides and the results of its use for restoring the pre-landslide stress state using the example of one of the tragic landslides. The numerical finite element algorithm of studying the stress–strain state (SSS) of soil deposits of slopes of the inclined-layered structure is briefly described, with specific features of the use of isoparametric elements of the quadrangular shape with four nodes of arbitrary shape. For detailed studying the SSS, the cover soils of the steep slope of the inclined-layered structure, in height from the arch to the foot, are conventionally divided into three zones, each of which has layered structures. Studies of the geometry of its area and the angle of inclination of the slope showed that the two-layer structure of its original structure made a curved path repeating the outline of the gorge. The finite element method helped to model the soil deposits of the slope with the granite-basalt rock as close as possible to the landslide initial shape. The proposed methodology, the mechanical-mathematical model, algorithms and calculation examples allow predicting the possible occurrence of landslides on other countless hillsides of the Northern Tien Shan by determining stress concentration zones.