We consider the statement of a stochastic boundary value problem corresponding to the non-elastic deformation of lamina composite materials of random structure. This problem is of importance for the prognosis of nonlinear behavior of laminated carbon-plastic materials reinforcing by fibers at various angles. The material functions that determine the non-elastic behavior of a lamina can be obtained on the basis of solution of a set of inverse problems for cross-ply reinforced plastics with various angles of reinforcement. At that, we use the experimental data corresponding to unidirectional tension. These experiments are considered as the tests for a monolayer under the action of various stress-strain states. We present the comparison of the results obtained experimentally and theoretically. The effective strain curves are obtained for elastic schemes of loading.