To ensure the certainty of results concerning Eigen frequencies values of a rectangular plate resting on the surface of an elastic half-space with inertial properties obtained numerically, verification is achieved by applying the principle of superposition method. To accomplish this operation, one must first determine the signal Tj(t) representing the sum of the amplitudes of the first Eigen modes at a point j of a plate. By applying the previously established signal formula of the modal method over a given time interval, the graph of the searched signal at a centre of any element of the discretized plate can be drawn. By studying the inverse problem of the obtained signal, through the application of the Fast Fourier Transform (FFT) via an appropriate computer code developed on Mathematica software, enabled spectrum location of the values of the Eigen frequencies of the plate in terms of the magnitude of the FFT. In this study, reading the obtained peaks of the spectrum allowed localization of the values of the first 16 Eigen frequencies of the studied plate. The natural frequency values of the studied plate were successfully verified by the principle of modal superposition.