A numerical method of solving spatial problems involving homogeneous isotropic bodies of revolution which obey the equations of flow theo:y and are under a non-axially symmetric load is developed. The method makes use of an algorithm in which a step is made in the load mad iterations are carried out on this step. The Ritz method is used to solve the elastic problem at each iteration. In this method, an expansion in a system of trigonometric functions along a peripheral direction and with respect to the coordinates in the meridian plane is used, that is, a two-dimensional finite-element approximation. It is proved that the iterative process converges in the case of an isotropically hardening body which obeys the associated flow law subject to the Mises plasticity condition. Sufficient conditions for the Ritz solution to converge, on iteration, to the exact solution are also obtained both in the case of external aad internal problems. The method is used to calculate a preloaded elastoplastic haft-space with a blind hole as the load applied to the lateral surface of the hole is removed. The problem simulates the process of boring a hole in a body which is used to determine the residual messes in it. A comparison is made between the results obtained and the results of the solution of the ~ame problem in an elastic formulation which is used in practice at the present time to determine residual stresses.