Nonlinear random vibration of the cables with small sag-to-span ratio and excited by in-plane transverse uniformly distributed Gaussian white noise is studied by a nonlinear multi-degree-of-freedom system which is formulated with Galerkin's method. The stationary probabilistic solutions of the nonlinear system are analyzed with the state-space-split method in conjunction with the exponential polynomial closure method. Effectiveness of this approach about the cable random vibration is examined through comparison with Monte Carlo simulation and equivalent linearization method. The probabilistic solutions of the cable random vibrations are also studied by modeling the cable as single-degree-of-freedom system and multi-degree-of-freedom system.