Abstract: A theoretical model is derived which describes the non-linear response of a stay cable to the lateral oscillation of bridge deck. The motion equations of stay cables, which are established based on Hamilton’s principle, are solved approximately using the multiple scale method. In the analysis of a real stay cable, the effects of excitation amplitude, frequency and damping etc are discussed. The results are also compared with those obtained through numerical simulation. It is shown that large amplitude vibration of the cable may be caused by lateral oscillation of the deck, and the non-linear characteristics of the cable’s vibration, such as multi-value, jumping etc are obvious.