Thus, mathematical model stressed- strained of a condition of layered masses is constructed. The model has high accuracy. It allows to simulate slippery contact of layers without friction. Thus not the order of permitting system of the equations is increased, and at its realization the method of fenite elements does not increase quantity of required degrees freedom. The differential operators included in system the equations are similar known in the classical theory of shells. It facilitates construction of a finite element. Presence in system of the differential equations of derivative of external forces allows to use her for the decision of contact problems with a stain of contact commensurable with thickness of a masses.