Phenomenological models of mechanochemical corrosion kinetics and their application to the prediction of lifetime of thin-walled cylindrical and spherical shells under internal and external pressures and temperatures are discussed. Closed-form solutions for one- and double-sided corrosion are developed in a compact form that, nevertheless, may reflect various temperature effects such as its influence on the corrosion rate, corrosion inhibition, maximal allowable stress of the shell material, coating lifetimes, and, by changing the thermo-elastic stresses, on the mechanochemical effect and the bearing capacity factor.