Calculations of strength, stability and vibration of shell structures play an important role in the design of modern devices machines and structures. However, the behavior of thin-walled structures of variable thickness during which geometric nonlinearity, lateral shifts, viscoelasticity (creep) of the material, the variability of the profile take place and thermal deformation starts up is not studied enough. In this paper the mathematical deformation models of variable thickness shells (smoothly variable and ribbed shells), experiencing either mechanical load or permanent temperature field and taking into account the geometrical nonlinearity, creeping and transverse shear, were developed. The refined geometrical proportions for geometrically nonlinear and steadiness problems are given.