Abstract: In this paper, the stochastic differential equations ofstay cables under axial narrow-band random excitations are derived with theconsideration of cable sag and variation of cable tension along cables.Gaussian and the first order non-Gaussian closure solutions are deduced withthe cumulant closure scheme. A numerical case of the cable A20 with a lengthabout 330\,m of No.2 Nanjing Bridge over Yangtze River is carried out toobtain the cable vibration response. Monte-Carlo method is applied to verifythe theoretical solutions in the present work. Moreover, the effects ofexcitation frequency on the vibration response of the cable are investigatedwhen the ratio value of the central excitation frequency to naturalfrequency of the cable is 1 or 2. Some new conclusions are summarized in thepresent study.