Based on one dimensional constitutive equations of Revlon materials and the motion equations of the cable, the partial differential equations of the viscoelastic cable in inner and outer of plan under the gravity are investigated. Using Galerkin's method, a system of nonlinear ordinary equations is obtained. The analysis methods of the dynamic stability of viscoelastic cable are given. Finally, the effect of dynamic response of the cable, which is produced by elastic and viscoelastic parameters, is testified by the research of digital simulation.