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An evident elastic anisotropy is an inherent background for anomalous physical properties and a wide range of applications for the majority of newly developing engineering materials (polymers, composites, ceramics, nano-structures, etc.). As a result, their mechanical performance strongly depends on the orientation of the loads applied and therefore requires detailed information on material stiffness anisotropy. The ultrasonic measurement of stiffness anisotropy is a time consuming procedure which requires cutting material in pieces and testing a number of specimens of various orientations. Mechanical performance of plate-like materials and components, typical for automotive and aviation industries, depends mainly on the in-plane anisotropy of stiffness. In ultrasonic frequency range, the velocity anisotropy measured by using the bulk wave is independent of frequency and fully determined by elastic moduli of material. In plate-like anisotropic materials, the velocity in-plane anisotropy is not constant but a function of frequency even for materials deemed to be homogeneous and non-dissipative. The reason for that is concerned with velocity dispersion which affects the wave propagation in different ways for various azimuth directions and thus modifies the elastic anisotropy pattern. Such an effect of dispersion of elastic anisotropy is of importance in dynamic testing and elastic wave applications of anisotropic materials