Abstract: Through theoretical study on the behavior of guided SH wave propagating along the circumferential direction of a hollow cylinder, based on the cylindrical coordinate system, the dispersion equation of guided SH wave was obtained by the derivation of Naviers equation. The numerical dispersion curves were calculated on Al hollow cylinder with ratios of internal to external radius as 0.3, 0.5 and 0.7. The results indicated the higher-order SH modes were more obvious than the lower-order SH modes in dispersion. So there are some advantages in applying the SH mode of the lower-order compared to the higher-order.