This article studies the aerodynamic induced vibration of stay cables (in cable-stayed bridges) under the combined effect of light wind and rain in terms of a section model with a dynamic rivulet oscillating on a moving cable perimeter in a steady wind. The motion of the cable section is coupled with the motion of the rivulet via aerodynamic fluid–structure interactions. These complex interactions are modelled in two distinct ways and the resulting cable motions compared. The first employs an approximation that permits the use of data extrapolated from wind-tunnel measurements. The second approaches the aerodynamic interaction in terms of a sub-critical vortex description. In the first approach the stability of the linearized system is reduced to a six-dimensional eigenvalue problem and the dependence of the eigenvalues are explored numerically as a function of parameters that enter into the model. The predictions of the model rely on measured data for drag, lift and torque coefficients for fixed experimental cylinders with attached artificial rivulets, and data for the equilibrium location of rain-induced rivulets. In the second approach the dynamical evolution of the non-linear system of differential equations is explored and the results compared with those obtained in the first model. The results offer a useful means to understand how rain-wind induced vibrations of stay cables can arise and persist in terms of more realistic models than have been considered before in the literature.