A numerical method for the analysis of the stress-strain state and strength of a thin-walled structural member subject to increasing internal pressure is proposed. It is based on the constitutive equations describing the elastoplastic deformation of isotropic materials along small-curvature paths and taking into account the stress mode, the theory of thin shells of revolution, failure criterion, and a method to solve a boundary-value problem of plasticity. Numerical values of the critical load are found Keywords: elastoplastic deformation, shells of revolution, failure criterion, critical load Introduction. Thin-walled high-pressure vessels are structural members of aircraft, vehicles, etc. The stress-strain state (SSS) and strength of such structural members were studied in [9-11, 13, 16-19, etc.]. The strength of high-pressure vessels depends on many factors, including geometry, material properties, loading conditions, etc. The material properties are known to strongly depend on the stress mode in some cases, which is manifested, for example, as a difference between the tensile and compressive stress-strain curves [20][21][22].Here we will assess the effect of the stress mode on the critical load for a specific thin-walled member of a critical structure. To this end, we will solve, step by step, the axisymmetric problem of plasticity for a thin isotropic shell modeling the structural member under consideration, with and without regard to the stress mode. We will use the constitutive equations describing deformation along small-curvature paths and either incorporating [1,7,14,15] or disregarding [5, 23] the stress mode. The calculated quantities describing the SSS of the shell will be used to validate the failure criterion formulated in [4] and to determine the critical internal pressure.Note that the papers [6,8,12] describe methods for and the results of solving the axisymmetric problem of plasticity for thin isotropic shells using the theory of deformation along small-curvature paths and taking into account the stress mode, but do not evaluate the strength of these shells. Contrastingly, we will determine, step by step, the elastoplastic stress-strain state of a shell, taking into account the stress mode, and will evaluate its strength.1. Problem Statement and Basic Equations. Consider a shell of revolution that is initially in stress/strain-free state at constant temperature T T = =
