Abstract: A theoretical method for analysis of dispersion characteristics of SH-type SAWs propagating on periodic metallic grating structures was presented. Based on D.P,Chen and Haus theory, a variational principle and COM equation for the analysis of SH-type SAWs was used to investigate the dispersion characteristics of SH-type SAWs propagating on periodic metallic grating structures. It's merit is no need for complex Green's function and it's theoretical results are in agreement with that of Hashimoto's finite element method. Hashimoto's method is helpless for calculating the dispersion relation of short-circuited gratings of ST-90°X quartz etc, but the method developed in this paper can successfully calculate that.