The behavior of the plate systems in contact with the elastic medium, devoted a large number of works. Virtually no posts related to the calculation of such systems in an elastic medium, taking into account the non-linear stress-strain diagram of the material shells. This article is a further development of [1]. It is developed method of calculation of physically nonlinear laminate systems such as prismatic shells interacting with an elastic medium. To derive the differential equations of equilibrium using energy method. The final equations are implemented to numerical Runge-Kutta methods. As an example, the U-shaped system is in contact with the elastic medium. It presents an assessment of the effect of the elastic medium and physical nonlinearity on the stress-strain state of the plate.