Based on catenary systems of Xinjiang railway in strong wind area, the effect of kinematic nonlinearity and material nonlinearity of catenary systems was considered, and the finite model of catenary systems was discussed. It analyzed the catenary systems in nonlinear buckling instability by using the nonlinear analysis module of the software package ANSYS and Budiansky-Roth criterion. The buckling wind velocity in different situations of structure height, span, and the number of hanger was calculated and extracted after loading horizontal wind on catenary systems. Then it analyzed the influence of three parameters on static stability of the structure and confirmed the appropriate structural parameters according to the data results. The calculation result showed that it could obtain preferable stability by increasing the stiffness of the catenary support structure. The structure height and span had a great influence on load bearing properties of catenary systems: the smaller height and span were, the better static stability was; and the most appropriate hanger number was 8 considering structural stiffness and compressive deformation.