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In this work, we report theoretical and experimental results on the 8 lowest modes of plate acoustic waves (PAW) propagating along the x-axis in the Z-cut of LiNbO3 wafers (the "ZX-cut"). Dispersion curves are calculated by the method of partial waves and by the Finite Element Method (FEM); the curves are then measured experimentally. The spectra obtained by the 2 methods are in good agreement with each other and with the experimental results. The PAW modes are identified as components of the total acoustic displacements near cutoff frequencies. Electromechanical coupling efficiency of the 8 modes is described. The FEM work is verified by an application to the design and testing of a PAW delay line in a ZX-cut LiNbO3 wafer. These results may be useful for analysis of many devices fabricated in Z-cut wafers, such as acoustoelectric and acousto-optic components, ultrasonic motors and actuators, micro/nano-particle transporters, and other devices employing periodically poled ferroelectric waveguides.