Abstract: The strong coupled thickness-shear vibration and flexural vibration of the La₃Ga₅SiO₁₄ crystal plate are analyzed with Mindlin plate theory, and the dispersion relationships, spectrum relationships and vibration mode displacements of high frequency vibrations of La₃Ga₅SiO₁₄ crystal plate are obtained. The numerical results show that the first-order accurate cut-off frequency of thickness-shear vibrations of La₃Ga₅SiO₁₄ crystal plate can be obtained with the Mindlin plate theory without correction coefficients. According to the selection method of the optimal length/thickness ratio of chip design chip of the quartz crystal resonator, the optimal size of La₃Ga₅SiO₁₄ crystal wafer is determined to avoid the strong coupling bteween thickness-shear vibration mode and flexural vibration mode. By drawing the displacement diagrams of each vibration mode with the optimal size of La₃Ga₅SiO₁₄ crystal plate, it is found that the thickness-shear vibration mode is the main vibration mode with a good energy trapping effect. The application and analysis of Mindlin plate theory in the high frequency vibration of La₃Ga₅SiO₁₄ crystal plate can guide the practical research and development of La₃Ga₅SiO₁₄ crystal resonator.