The paper presents a computation procedure of physically nonlinear prismatic shells with the sealed ends. It is known that plates reinforced by stiffening ribs and located in the elastic medium can be calculated in a similar way as uniform ones (without reinforcements). In this case the effect of edges on the stress-strained state of plate was calculated in the form of the elastic support by Winklerian model. Thus, contact with the elastic medium was simulated, the medium was assumed in the form of a single-layer base. Dependence between the intensities of stresses and strains was established as a cubic polynomial. Fundamental differential equations were derived on the basis of the energy method. Final equations were realized by the numerical method of Runge – Kutta. Computation of U-shaped shell was executed on the basis of the obtained equations. Evaluation of the influence of elastic medium and physical nonlinearity on the stress-strained state of lamellar system was represented.