Abstract: Based on Kelvin-Voight viscoelasticity, the circumferential SH wave controlling equations of orthotropic viscoelastic hollow cylinders are deduced. The SH wave characteristics are controlled by two elastic constants and their corresponding viscous coefficients. By the first and second Bessel functions, the exact dispersion equation is obtained. The phase velocity dispersion curves and attenuation curves for four different ratios of outer radius to thickness are calculated. The influences of the ratio are analyzed. Then the cases of isotropic viscoelastic hollow cylinders are calculated to show their differences. The effects of the two elastic constants and viscous coefficients on the dispersion and attenuation are discussed.