Abstract: Based on the one-dimensional constitutive equation of Relvon materials and the motion equation of cables, the governing equations of the viscoelastic cables in the vertical plane are derived. By using the variable separation method, a linear ordinary equation is obtained, which is expressed by modal coordinates and has periodic coefficients. The dynamic stability criteria of the viscoelastic cables subjected to periodic axial loads are obtained. The regions of stability and instability are plotted for various sag to span ratios.