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Analysis of the frequency spectrum of circular elastic‐anisotropic and unelectroded AT‐cut quartz plates with free edges is performed by using the equation of the coupled thickness‐shear and thickness‐twist vibrations. It is found that the frequency spectrum of energy‐trapped vibrational modes can be obtained from the parametric zero relations of Mathieu functions, which are solutions of this equation. Experimentally measured frequency values of the fundamental and the first few harmonic overtones are in good agreement with theory.