The monograph is devoted to one of the sections of the mechanics of a deformable solid: the three-dimensional theory of stability of the equilibrium state of near-mountain workings for compressible and incompressible elastic-plastic and elastic-viscous-plastic models of rocks .. The results on linearized problems of the theory of plasticity of complex media by the method of small parameter. are presented. Within the framework of the general three-dimensional linearized theory of stability of small deformations, the theory of stability of mountain workings is presented, a general approach to solving cylindrical and spherical problems of stability of mechanics for these models is developed. Cases of horizontal and vertical workings, as well as underground cavities supported by multilayer fasteners are considered. The application of the theory to the deformation and stability of the wholes, drilling wells, layered arrays, shells with a filler, and t. d. Designed for specialists in the mechanics of rigid deformable body and rocks, teachers, graduate students and senior students of universities dealing with the issues of stability of spatial bodies and structures .