In this paper, an efficient analysis method considering both geometric and material nonlinearities is proposed for predicting the ultimate strength and behavior of multi-span suspension bridges. The geometric nonlinearities of the cable members due to sag effects are captured using the catenary element, while the geometric nonlinearities of the beam-column members due to second-order effects are captured using the stability functions. The material nonlinearities of the cable and beam-column members are considered using elastic-plastic hinge and refined plastic hinge models, respectively. A simple initial shape analysis method is presented to determine the deformed shape and initial cable tension of the bridge under dead loads. Numerical examples are presented to verify the accuracy and efficiency of the proposed method. In addition, a case study on a four-span suspension bridge is carried out to show the capability of the proposed method in estimating the strength and behavior of very large scale structures. (C) 2013 Elsevier Ltd. All rights reserved.