In this paper, we utilized a Stroh based formulation for solving problems of surface waves in layered piezoelectric media, and then, applied it to analyze surface acoustic wave (SAW) devices. The determination of the optimal cut of a piezoelectric crystal and the choice of the best propagation of SAW devices were given. The dispersion induced by a thin metal layer on SAW propagation in a SAW device was analyzed and discussed. Finally, we applied the formulation to calculate the effective permittivity and phase velocity dispersion of a LiNbO3/Diamond layered SAW device. Both of the null frequency bandwidth and the insertion loss of the dispersive SAW device were obtained.