The coupling of modes (COM) theory is widely used in the design and simulation of surface acoustic wave devices.The propagation characteristics of SAW in the periodic metallic grating structures have been analyzed by using the finite element analysis software and COM theory The coupling parameters of the dispersion characteristics,coupling coefficient,relative wave number and attenuation coefficient are obtained for different gate thickness in a short circuit or open circuit gate.With an increase in the gate thickness,the attenuation coefficient and stop bandwidth will reduce in a short circuit gate, but the open circuit gate is the opposite.