Abstract: The effect factors necessary to be considered in the study of mooring lines transferring from taut to slack are analyzed from the view of stress waves. The radio of mooring line gravity per unit to the horizontal tension is introduced. Based on Taylor series expansion, the horizontal tension and curvature are the function of and . Considering the effects of horizontal tension, the free propagation characters are analyzed, including the characteristic frequency, group velocity and dispersion relation, the effects of tension in cable, wave number, and coordinates of the cable. The research results indicate that, when the cable alters from slack to taut, the shifty tension, radius of curvature and the dead weight of the cable cannot be ignored. The work in this paper lays a foundation for future taut-slack problems.