This work aims to enhance the methodology for characterizing the elastic properties of massive sample. A novel methodological approach is coupled to the resonant ultrasonic spectroscopy (RUS). The innovation consists in a find-peaks function used to automatically extract resonant frequencies from the mechanical frequency response of the sample, and to a K-means clustering algorithm used to pool the data obtained from multiple spectra measured on the same sample. It results in a fully automated detection of all predicted resonant mode of a specimen and hence increase both ease of use and accuracy of the RUS method. The acoustic resonance measurements are carried out using two shear transducers having a center frequency at 2.25 MHz. In view to solve the inverse problem, two hypotheses are implemented, either isotropic or orthotropic. The obtained results show the validity of the proposed methodology for both assumptions and are in agreement with the literature.