In this study, the circumferential interaction behavior of the SH-wave with a piezoelectric cylinder coated with a viscoelastic material is investigated. The coating interface is imperfect and the viscoelastic material is subjected to pre-stress. By applying mathematical methods to the dynamical governing equations, expressions for displacement components and electric potential is obtained. Utilizing the set of boundary conditions, dispersion and damping equations are established for this model. The impacts of perfect & imperfect interfaces, piezoelectric & dielectric constants, initial stress, dissipation factor, attenuation coefficient and radial thickness ratio of materials on the phase and damped velocities of SH-wave are observed by numerical examples and graphical visuals.