The optimal design of quartz crystal resonators depends on the accurate analysis of thickness-shear vibrations of the plate with and without driving voltage across electrodes.Usually the plate vibrates in the thickness-shear mode demanding the consideration of length and width to evaluate the effect of aspect ratios under different frequencies and vibration modes.In other words,two-dimensional analysis of vibrations of the anisotropic plate is necessary in the design of quartz crystal resonators for the selection of optimal aspect ratios to obtain ideal vibrations.This is a challenge because analytical solutions are not generally available and numerical methods have to be utilized for the analysis with high accuracy due to the relatively high frequency and strong couplings of modes.The coupled Mindlin plate equations are one of the frequently used tools with extensive studies on the vibration analysis,but two-dimensional solutions have to be obtained with numerical methods under finer mesh schemes.In this study,we start with the fully modified Mindlin plate equations for electroded and unelectroded crystal plates and they are applied with details in the Comsol environment for easy implementation.