Abstract: A two-degree-of-freedom model of rain-wind-induced vibrations of cable structure with moving upper rivulet was studied. It is assumed that the frequency of the circumferential motion of the upper rivulet is equal to that of the cable. The original system was studied by numerical computation with symbol algebra language Mathematica. The influence of density of air, damping of cable, angle of yaw etc. was discussed. Solutions according to the similar problems in practical engineering were proposed. The phase diagrams of the cable and rivulet were achieved. It is shown that their moments converged to limit circles. A simpler averaging equation is achieved by virtue of Mathematica program, which showed the existence of stationary solutions.