Abstract: Transmitting boundary is a common method for boundary treatment in dynamic finite element analyses. In view of the transmitting boundary for finite element analysis of cylindrical shear wave in semi-infinite domain caused by torsional vibration, two kinds of viscoelastic transmitting boundaries are proposed through two kinds of approximate derivation, and their calculation accuracy is analyzed through comparative computations. The numerical analysis results show that the two kinds of viscoelastic boundaries can well simulate the infinity of foundation in torsional vibration analysis. At the same time, for the torsional vibration considered here, the accuracy of the transmission boundary is higher when the spring stiffness in the viscoelastic boundary condition is equal to the actual static stiffness.