The laboratory work of students is aimed at obtaining analytical and numerical solutions to the problem of expanding with a constant velocity of a spherical cavity from a point in a boundless elastic-ideal plastic medium. Particular attention is paid to the process of reducing the initial boundary problem for a system of two equations in first-order partial derivatives to the boundary problem for a system of two ordinary first-order differential equations by means of automodel transformation .. A comparison of the analytical solution under the assumption of incompressibility of the medium with the numerical solution for two cases of boundary conditions. The applications contain algorithms for numerical solution of initial and boundary problems by shooting and Runge-Kutta methods, a table of material parameters, the text of the program in the C++ programming language. Intended for students studying in the direction of training 01. 03. 03 "Mechanics and mathematical modeling" .