In the textbook analytical and numerical solutions of problems on expansion of a spherical cavity in elastic-plastic media for different models of media are considered. The process of reduction of the system of equations in partial derivatives to the system of ordinary differential equations by means of automodel transformations is shown in detail, in some cases analytical solutions. are obtained. The application contains algorithms for numerical solution of initial-edge problems by shooting methods and Runge-Kutta . Designed for students studying in the direction of training 010400 "Applied mathematics and computer science", 010800 "Mechanics and mathematical modeling" .