Shells as elements of various structures are widely used in different fields of engineering and construction. Thin-walled elements of modern structures that represent shells designed to work under the influence of mechanical stress, which can be either static or dynamic. Calculations of strength, stability and vibrations of shell structures have an important role in the design of modern devices, machines and constructions. Profile of shell can have smooth thickening to increase rigidity in some areas. There is also a variant of a thin-walled part of the shell strengthening by discretely spaced ribs.In both cases, carrying force of structures significantly increases with a slight increase of its mass. In this article geometrically nonlinear mathematical deformation models of shells with variable thickness, in particular ribbed shells, (for static and dynamic problems) are proposed. Different material properties are taken into account (orthotropism, linear and nonlinear elasticity, viscoelasticity and creeping), as well as transversal movements, variable rigidity of ribbed shells besides its finite widths and height of ribs, shear and torsion rigidity.