Long span cable-stayed bridges can inherently undergo to geometric and material nonlinear behavior when subjected to extreme events. In the current research the local post buckling behavior of the bridge deck under seismic loading has been investigated. Simulations have been carried out using an explicit dynamic method for a three dimensional finite element model of cable-stayed bridge. A comprehensive parametric study has been conducted on dynamic characteristics of bridge. By using beam element with low bending stiffness in the simulations some of bridge’s dynamic parameters such as natural frequency and vibration mod shape have been estimated through selection and the development of cable finite element model. In this study, based on frequency analysis, natural frequency of bridge has been estimated in a range of 1-0.2 Hz. Seismic response of bridge to ground motions was investigated for several earthquakes in two cases of uniform and non-uniform input supports. Also the bridge behavior under seismic loads has been studied considering small and large deformations. Results show a considerable difference in seismic response of long span cable-stayed bridge in cases of geometric linear and non-linear behavior. Non-linear behavior of deck material was investigated considering uniform and non-uniform spatial earthquake under geometrical linear and non-linear analysis. Results also show that seismic response of bridge, considering non-linear and linear behavior of deck material had no significant difference. Also the effect of bridge deck’s main span length on seismic behavior was investigated. According to the results increasing of main span length do not necessarily lead to increasing of stresses and forces in bridge components. In addition, a comprehensive parametric study was conducted considering cable pre-tension force and flexibility of foundation. Also parametric seismic studies, considering uniform and non-uniform ground motions of several earthquakes using linear and non-linear geometrical dynamic analysis, were conducted. Response of bridge did not increase with increment in deck negative sag and foundation flexibility and response of bridge is dependent on earthquake record and consisting frequency. According to the previous analysis the local post buckling of bridge deck was studied. Results show that in case uniform ground motions of considered earthquake was investigated, considering large deformation, part of deck entered to local post buckling.