To perform three dimensional nonlinear static analysis of suspension bridges, this study suggests a finite element method. All sources of geometric nonlinearity are considered in the analysis. Geometric nonlinear frame elements which can consider flexural-torsional coupling effects and have seven degrees of freedom at each node including warping are used to model stiffening girders and towers. Main cables and hangers are modeled by geometric nonlinear cable elements based on exact solution of self-weighted elastic catenary cable theory. As a prerequisite to the analysis of suspension bridge, a method of establishing initial static equilibrium state due to dead loads is proposed. Examples of mathematical models of actual bridges are presented. The results show that initial equilibrium states of two types of suspension bridge can be determined properly according to the presented method. It is found that these flexible structures are highly nonlinear. Present study is essential to start linear or nonlinear dynamic analysis of suspension bridge subjected to important dynamic loads such as wind loads, earthquake loads and moving vehicle loads.