The history of calculating the stability of landslide-prone slopes dates back 250 years. Most of them are simplified methods for calculating the stability of landslide bodies of a sequent and consistent type. The weaknesses of this type of method were noted by the authors themselves. These shortcomings remain in several recently created computer programs, specially designed for landslides and do not consider the stress-deformed state analysis of the landslide body. In most of the methods, the stability of the slope is evaluated under the conditions of limit equilibrium, Coulomb-Mohr and similar strength theories, and the influence of the time factor can only be reflected indirectly. This was called the "Shear Strength Reduction Factor". Consideration of the "shear strength reduction factor" is very important when calculating the stability of block-type coherent and inconsistent landslide bodies that maintain a completely stable state for a long time and suddenly lose their stable equilibrium because of extreme meteorological or other effects. Creep plastic deformation is more rheological in nature because deformation can occur very rapidly/or slowly in periods ranging from a few hours to a hundred years. It depends not only on the strength but also the deformation characteristics of the rock. These can be determined by laboratory testing of samples of geological material. The means for its full use will be created after the creation of the apparatus for the direct analysis of self-creeping plastic landslides. So, in all these directions, the development of methods for calculating the stability of landslide bodies is a scientific-technical problem. By authors, the original numerical-analytical version of the method of assessment and calculation of stability of landslide bodies, both consequent and nonconsequent, has been developed, with the joint use of stress analysis equipment and computer programs. In contrast to the existing methods, the developed method enables the modelling of calculation schemes of various forms of possible collapse of landslide-prone bodies based on the analysis of the stress-deformed state of the stratified structure. It considers the necessary measures to ensure their stability in normal and extreme conditions under the action of gravitational and seismic forces should be calculated.

Landslide, stability of prone, numerical-analytical method, creep-plastic deformation