A method is proposed for determining the service life of a metal shell structure under variable thermomechanical loading. The operating stresses are determined by solving a nonlinear boundary value problem for a thin-walled shell of revolution. The service life of a metal structure under variable thermomechanical loads and taking into account contact with an aggressive environment is determined using the equations of low-cycle material fatigue. The method is demonstrated on the design of a muffle intended for high temperature annealing of electrolytic steel.