Abstract: The catenary element has higher precision than other elements in nonlinear analysis of cable-stayed bridges.Based on the self-weight constraint equation,a method of accurate catenary iteration is developed to find the initial states of main cables of cable-stayed bridges with two design parameters known in advance.The proposed method can calculate the self-weight density variations of cables.Based on the mechanical characteristic of cable saddle,explicit tangent stiffness equations relating cable tension and saddle offset are deduced,and the accurate formulas of non-stressed cable length on saddles are also obtained.The example results show that the proposed method is accurate,stable and quickly convergent.