The spatial three dimensional variation of the polarization ellipse characterizing an elastic movement of the solid particles in the harmonically oscillating ultrasonic fields is studied. Such a variation comes into sight because of the interference of various elastic modes generated during the excitation and/or scattering of acoustic waves by the inhomogeneities located on the solid surface. In order to confirm this effect, an innovative method based on finite element approach is used showing a rule to find the form and orientation of the elastic polarization ellipse in general case. Polarization plane may have an arbitrary orientation in anisotropic crystals. The dispersive parameters of the spatially changeable ellipse of polarization in a substrate with perturbed boundary conditions depend on the polarization and on the relative complex-valued amplitudes of the partial elastic modes which contribute differently to the sum of acoustic fields at every point of analysis. Results of a detailed investigation of the mentioned effects in an interdigital transducer formed by aluminum electrodes on the ST-X cut of quartz substrate are presented.