This paper describes the method for the determination of the elastic constants of composite materials from the experimental results for eigenfrequencies of the plates. In this work it is proposed to use the numericalexperimental identification method. The identification procedure is based on the method of experiment design, the response surface approach and the finite element method. The main advantage of this method is significant reduction of the number of computations of the criterion. The finite element modeling is performed only in the reference points. Therefore, a significant reduction in calculations of the identification functional can be achieved in comparison with the conventional methods of minimization The functional to be minimized describes the difference between the experimentally measured and numerically calculated eigenfrequencies, which are dependent on parameters to be identified. The identification parameters are five elastic constants of material. By minimizing the functional the identification parameters are obtained. The method is employed to identify the elastic properties of angle-play laminates.