Cables are used for many engineering applications such as transport systems that involve mobile cables suspended between supports for carrying attached vehicles. Because of the inherent cable’s flexibility and the modification of dynamics properties during movement, such systems are sensitive to self sustained oscillations under steady-state conditions. To provide an understanding of such vibratory excitation sources and a design method to prevent operating problems, this paper proposes a real case study of a chairlift and the development of an original model. The aim is to highlight the mechanisms responsible for the dynamic response amplification of the cable line. The method is based on a reduction of the complete dynamic model to a single mode which localises the vibration energy along the cable loop. The reduced model thus obtained takes the form of a Mathieu-Hill parametric excitation oscillator. The stability study reveals zones of instability in which the dynamic system response increases. The approach is then validated on the real case study by positioning the chairlift’s operating points in the stability diagram according to different configurations. Operating points are determined using the signal of the evolution of the static tension of the cable during the movement of the vehicles. Based on the case study, a general methodology for modifying design parameters is proposed to avoid undesirable line dynamics.