Amplitude-frequency characteristics of the piezoceramic elements in the forms of a thin plate and a rod are studied through ANSYS program. Resonance and antiresonance frequencies of the first two disk radial modes, the thickness mode of the thin plate, and the axial mode of the rectangular cross-section long rod are measured. The numerical results are compared to the known determination techniques of the elastic Sij, piezoelectric dij, and dielectric εij constants of the piezoelectric materials. The improved procedure for determining elasticity constant SE13 on one specimen of only radial disk oscillations is suggested and substantiated. The method is based upon the relationships between the elastic constants of piezoceramics and the dispersion of longitudinal waves. The new method usage domain is studied. As compared to the known techniques, the proposed method facilitates the measure procedure and allows determining the elastic constant with the extended precision. A fundamentally new technique of measuring resonant and antiresonant frequencies of piezoelements with losses is developed for defining a full range of material constants of ideal elements without losses according to the Russian branch standards and the Institute of Radio Engineers (USA) standards for piezoelectric crystals.