Based on CR formulation superposition method for geometrical nonlinear analysis,the catenary cable element was used to simulate stay cable.

By analyzing all kinds of analysis theory of cable stays,the problems about cable stays were divided into two kinds,and based on the theory of catenary cable element,a unified analysis theory of cable stays was put forward.

In this paper, we used catenary cable element imitate the cable, use the theory which is based on the CR formulation effects and considered the beam-column effect and the large displacement to establish of space model.

Based on the analytical model of catenary, the analysis model of self-anchored suspension bridge was set up for iteratively calculation of the main cable shape and the unstressed length of the main cable, by simplifying stiffening girder to rigid support continuous girder and utilizing the function between the element projections and the cable force components at the catenary element ends.

The stiffness matrix and node force vector of the elastic catenary element can be gained,and the equilibrium equation of the struct.

With the functional relationship between cable element projection and element nodal force of catenary element,bridging shape and stressless length of main cable for suspension bridge are calculated by iterative method.

With comparison,the catenary element is most efficient for precise description of the static configuration,while the straight rod element is rough and the multiple joint element,though works more precisely,makes the computation more complicated.