The probabilistic solutions of the responses of shallow cable are studied when the cable is excited by filtered Gaussian white noise. The nonlinear multi-degree-of-freedom system is formulated which governs the random vibration of cable. The state-space-split (SSS) method and exponential polynomial closure (EPC) method are adopted to analyze the probabilistic solutions of cable systems in order to study the effectiveness and computational efficiency of SSS-EPC procedure in analyzing the probabilistic solutions of the cable systems under the excitation of filtered Gaussian white noise. Numerical results obtained by SSS-EPC method, Monte Carlo simulation, and equivalent linearization method are compared to examine the computational efficiency and numerical accuracy of SSS-EPC method in this case. Thereafter, the behaviors of probabilistic solutions of the cable systems are studied with different values of peak frequency and seismic intensity of excitation when the cable is excited by Kanai-Tajimi seismic force. Some observations and discussions are given by introducing a probabilistic quantity to show the influence of excitations on the probabilistic solutions.