The problem of a straining of layered shells of the variable thickness reinforced by fibers of a constant cross-section and working in conditions of steady creep of all a component metal-composition is formulated. The system of the resolving equations and boundary conditions matching it is analyzed. The method of the solution of a problem in view is developed. The way of an approximate solution of such problems to conditions of unsteady creeping is specified. The concrete calculations, which have shown, are lead, that compliance of thin-walled constructions in conditions of the steady creeping essentially depends on structure of reinforcement, and the separation of base layers in shells of the big curvature not always gives a significant positive effect.