In this paper,the coupled extension and thicknesstwist vibrations are studied for AT-cut quartz plates under Lateral Field Excitation(LFE)with variations along the x1-direction.Mindlin’s two-dimensional equations are used for anisotropic crystal plates.Both free and electrically forced vibrations are considered.Important vibration characteristics are obtained,including dispersion relations,frequency spectra,and motional capacitances.It is shown that,to avoid the efects of the couplings between extension and thickness-twist vibrations,a series of discrete values of the length/thickness ratio of the crystal plate need to be excluded.The results are of fundamental significance for the design of LFE resonators and sensors. In this paper, the coupled extension and thicknesstwist vibrations were studied for AT-cut quartz plates under Lateral Field Excitation (LFE) with variations along the x1-direction. Mindlin’s two-dimensional equations are used for anisotropic crystal plates. vibrations are considered.Important vibration characteristics are obtained, including dispersion relations, frequency spectra, and motional capacitances. It is shown that to avoid the efects of the couplings between extension and thickness-twist vibrations, a series of discrete values ​​of the length / thickness ratio of the crystal plate need to be excluded the results are of fundamental significance for the design of LFE resonators and sensors.