This paper describes the characterization of SAW propagation in layered substrate and overlayered structures. The software based on the finite element method and spectral domain analysis was newly developed and applied to the characterization of SAW propagation under an infinitely-long Al interdigital transducer on a rotated Y-cut LiTaO(3)/sapphire substrate. Because of the finite LiTaO(3) thickness, a series of spurious resonances appears. It is shown that the excitation strength of the spurious resonances changes with frequency as well as the rotation angle, which reflects the frequency and rotation angle dependence of the energy leakage. Next, the analysis was carried out for SAWs propagating in a SiO(2) layer/Al IDT/42 degrees YX-LiTaO(3) structure. It is shown that the influence of the SiO(2) layer is significantly dependent on the location where the SiO(2) layer is deposited. In particular, it is shown that when the SiO(2) layer is deposited only on top of the electrodes, the SAW reflectivity increases compared with when the SiO(2) layer is deposited between and on top of electrodes.