A theoretical model of transverse waves propagating on piezoelectric plates of finite thickness under metal strip gratings is proposed. Different mechanical and electrical boundary conditions are considered and their influence on the propagation characteristics of the waves is emphasized. In all the cases, the dispersion curve relating the angular frequency to the wave number exhibits more than only one stopband as found in the usual analysis of surface transverse waves on semi-infinite substrates. This model has been used to calculate the resonance frequencies of synchronous devices on AT-cut and Z-cut quartz plates. These theoretical predictions are compared to experimental results obtained using synchronous devices built on 128-μm-thick Z-cut plate of quartz and AT-cut plate of quartz and operating at frequency range 80–150 MHz.