<p>This paper investigates the propagation characteristics of thickness-twist (TT) and face-shear (FS) waves in a lithium niobate (LiNbO₃) plate covered with an elastic layer. The three-dimensional (3D) theories of piezoelasticity and that of isotropic elasticity are employed to analyze the LiNbO₃ plate and the elastic layer, respectively. A transcendental frequency equation governing the dispersion relations of the TT and FS waves is derived. The dispersion curves are plotted based on the derived transcendental frequency equation. The effects of the stiffness ratio, thickness ratio, and density&#xa0;ratio of the elastic layer relative to the LiNbO₃ plate on the cut-off frequency of the TT waves are analyzed. The results obtained in this work furnish important theoretical and practical guidance for the design and performance optimization of LiNbO₃-based devices.</p>