Abstract: The study on the propagation characteristics of stress waves is crucial to estimate the dynamic stability of project construction. Based on the excavation blasting tests on the basalt rock mass with columnar joints and considering the creep and stress relaxation characteristics of rock, an equivalent standard linear solid model for rock mass joints is proposed. By using the displacement discontinuity method, the propagation equation for obliquely incident stress waves across viscoelastic joints is carried out. Then the propagation characteristics are studied. The reflection coefficient increases with the increase of the frequency of incident waves, but the transmission coefficient decreases rapidly. As the incident angle increases within the critical angle, the transmission coefficient of converted waves (T_sp or T_ps) has the smallest value and increases at first then decreases, while the reflection coefficient of converted waves (R_sp or R_ps), and R_ss(R_pp) decreases at first then increases, but T_ss(T_pp) basically has no change. Complex energy transfer happens when the stress waves cross the viscoelastic joints. The energy between R_ss(R_pp) and R_sp(R_ps) transfers to each other, then reaches their extreme points almost together when the incident angle is close to a certain value. The energy of the same kind of waves is been transferred to that of converted waves as the incident angle increases. But the same kind of waves have much more energy than the converted waves all the way.