Abstract: Cable structures are widely used in electrical, civil, marine and aviation engineering. As cable in engineering longer and longer, the high-order vibration becomes more and more obvious. Accordingly, the disturbance propagation should be considered in the study. In the existing research on the propagation of elastic waves in cables, the damping is usually not considered. However, damping has an important influence on the propagation of waves. We developed the motion equation of three-dimensional elastic cable by considering damping into equation. The free propagation characteristics of in-plane and out-of-plane waves are discussed respectively by solving the equations of motion above, including frequency relation, phase velocity, group velocity. And then, the wave propagation law of the cable is further discussed by calculating the displacement response under the initial cosine pulse. Besides, we study the wave dispersion and the influence of damping on the propagation of elastic waves in cables. The results show that both in-plane and out-plane waves are dispersive while damping is considered. In addition, the in-plane waves are highly dispersive with the curvature considered. In addition, the crest of wave dissipates in wave propagation, and the response of trailing edge is higher than the leading edge while damping is considered.