Abstract:The governing equations of nonlinear free vibration of a horizontal c able were presented considering the effects of the bending stiffness, sag and th e geometric nonlinearity. Those partial differential equations were then transfo rmed into a set of ordinary differential equations through the Garlerkin method. Aimed at whether to consider the sag and geometric nonlinearity, four kinds of theories were put forward such as linear theory without sag, linear theory with sag, nonlinear theory without sag and nonlinear theory with sag. The harmoni c balance method was used to study the approximate analytic solution of the natura l frequency of cable vibration. The results agree well with those derived from t he method of the RungeKutta integration. Based on the comparative study on the four present theories, the quantitative decision was proposed to evaluate the in fluence of the bending stiffness, sag and nonlinearity on the natural frequency.