The relationships existing between the elastic constants and the frequencies of the natural modes of vibration of a finite plate of homogeneous material have never received a rigorous formulation. On the other hand, the solution of the relationships between elastic constants and natural frequencies of an infinite plate is rigorous;In the evaluation of the elastic constants of a material, an infinite plate can be approximated, either by making use of large, thin quartz plate or by using harmonica of the fundamental modes of vibration. The latter method was used in this investigation because of its greater accuracy;When a crystal plate is vibrating with a fundamental mode or a harmonic of this mode, the wave planes of the standing waves which are produced are parallel to the surfaces of the plate. Thus, as the order of this harmonic becomes progressively higher, more wave planes are crowded between the surfaces of the plate, and so the size of the plate becomes larger in comparison with each wave length, approximating ever closer the theoretical infinite plate. (Abstract shortened by UMI.)