This article constructs a stochastic model for the response of stay cables of cable-stayed bridges to the combined effect of wind and rain. It describes a spring-mounted section model of a stay cable in a steady wind where aerodynamic forces are modified by the dynamics of a mobile liquid rivulet. The motion of the rivulet is described by a simple stochastic process that, together with aerodynamic forces, models the complex fluid–structure interaction. Based on measured data for drag and lift coefficients and a static rivulet location, an analysis of the model suggests a new stochastic excitation mechanism for the rain–wind induced vibrations of stay cables.