The high frequency vibrations of plates have been studied for focused applications in the design of piezoelectric crystal resonators which are the key element of frequency control devices and sensors.With piezoelectric plates vibrating at the thickness-shear mode.analyses important to the resonator design have been done by the Mindlin plate theory [1].which has been adopted with improvements [2].The linear equations of Mindlin plate theory have been utilized for the calculation of vibration frequency and mode shapes for the optimal selection of piezoelectric plates of a quartz crystal resonator, while many other important parameters of a resonator.