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When constructing a mathematical model describing the inelastic non-isothermal deformation of the inner wall of the cylindrical shell of the combustion chamber of a liquid-propellant rocket engine (LRE ЖРД), a simplified design scheme of a one-dimensional stress-strain state (SSS НДС) of a bimetallic shell was used. The analysis of changes in stresses and deformations in the inner and outer walls of the shell during the periods of start-up, operation, shutdown and pause between starts of a multiple-action LRE is carried out. To describe the inelastic deformation of the inner wall, a mechanical analogue is used, which makes it possible to describe the non-isothermal processes of plasticity and creep. An example of calculating the stress-strain state of a shell is given, which makes it possible to estimate the accumulation of the absolute value of inelastic deformation in the material of the inner wall, which affects the damageability of its material. [ABSTRACT FROM AUTHOR]