There is developed an algorithm to determine position of possible exfoliations of a triple-periodic system of elastic inclusions from an elastic matrix of a metamaterial after its production. For this aim there is used the irradiation of each side of a cubic specimen of the metamaterial by short impulses with a tone filling with the ultrasonic longitudinal waves. The algorithm implies the experimental and the theoretical study of the propagation of a high-frequency wave through the periodic system of inclusions. The theoretical solution is constructed by methods of the geometrical diffraction theory. Based on comparison of the experimental data and the theoretical calculations there is evaluated the presence of exfoliations and their position inside the metamaterial.