A numerical-experimental method for determining the mechanical properties of shale composites has been created. The main principle of this method is the simple creation of mathematical models (response surfaces) using the results of calculations of the finite elements in the experimental plan points. Thus, a significant (50-100 times) reduction of the functional identification of the identification compared to the accepted minimization methods. This method is used for composite, laminated, sandwich type, etc. the determination of the elastic and viscous properties of materials from vibrometry experiments and the determination of the plastic properties of polymers from hardness tests.