stresses, deformation, plasticity, elasticity, spherical cavity.

The algorithm of successive approximations is developed for the analytical determination of the stressed state of a compressible elastic-plastic space with cavities. In the formulation of the problem inside the cavity pressure is absent, and at infinity mutually perpendicular forces are applied. The problem is solved by the method of a small parameter, in a spherical coordinate system, in dimensionless units of length. Three cases are considered under which conditions for complete plasticity can be satisfied, one of which corresponds to a spherical cavity. The zero values of the stresses in the elastic and plastic regions are determined, the zero approximation of the boundary of the elastic-plastic zone for the case of a spherical cavity, and also the first approximations of the stress components in the plastic region for three cases satisfying the condition of complete plasticity. The obtained results can be used in the field of mining, construction mechanics and other related fields.

Maksimov Aleksey Nikolaevich e-mail: alexei.maksimow@yandex.ru, Ph. D., Assoc. Professor, Chuvash State Agricultural Academy, Cheboksary, Russia. Pushkarenko Nikolay Nikolaevich e-mail: stl_mstu@mail.ru, Ph. D., Assoc. Professor, Chuvash State Agricultural Academy, Cheboksary, Russia. Dereviannih Evgeniya Anatolyevna e-mail: jane-evgeniya@yandex.ru, Ph. D., Assoc. Professor, Chuvash State Agricultural Academy, Cheboksary, Russia. Dmitriev Yuri Petrovich e-mail: 14102010olga@mail.ru, Ph. D., Assoc. Professor, Chuvash State Agricultural Academy, Cheboksary, Russia.