Rain-wind induced vibration is an aeroelastic phenomenon that occurs on the inclined cables of cable-stayed bridges and arises due to the interaction between the unsteady wind loading and the formation of water rivulets on the cable surface. A new numerical method has been developed at the University of Strathclyde to simulate the influence of the external flow field on the rivulet dynamics and vice versa. The approach is to couple a Discrete Vortex Method solver to determine the external flow field and unsteady aerodynamic loading, and a pseudo-spectral solver based on lubrication theory to model the evolution and growth of the water rivulets on the cable surface under external loading. Results of this coupled model are presented, to provide detailed information on the development of water rivulets and their interaction with the aerodynamic field. In particular, the effect of the initial water film thickness and the angle of attack in plane on the resulting rivulets are investigated. The results are consistent with previous full scale and experimental observations with rivulets forming on the upper surface of the cable only in configurations where rain-wind induced vibration has been observed. Additionally, the thickness of the lower rivulet is found to be self-limiting in all configurations. The results demonstrate that the model can be used to enhance the understanding of the underlying physical mechanisms of rain-wind-induced vibration.