In this paper, the dynamic response of cable-stayed bridge loaded by a train of moving forces with stochastic velocity is investigated. The cable-stayed bridge is modelled by Rayleigh beam with linear elastic supports. The stochastic Melnikov method is derived and the mean-square criterion is used to determine the effects of stochastic velocity and cables number on the threshold condition for the inhibition of smale horseshoes chaos in the system. The results indicate that the intensity of the random component of the loads velocity can be contributed to the enlargement of the possible chaotic domain of the system, and/or increases the chances to have a regular behavior of the system. On the other hand, the presence of cables in cable-stayed bridges system increases it degree of safety and paradoxically can be contributed to its destabilization. Numerical simulations of the governing equations are carried out to confirm the analytical prediction. The effect of loads number on the system response is also investigated. (C) 2016 Elsevier Ltd. All rights reserved.