Cable stayed bridge is the kind of structure that is very sensitive to different dynamic loads such as: moving loads, wind load and especially seismic load. The paper shows a overall research on methods of seismic analysis, models of cable stayed bridge, models of soil-structure interaction. The research paper focuses on behavior of cable stayed bridge during earthquakes in which investigating the effects of soil-structure interaction (SSI) was done. In a particular example, the modeling of cable stayed bridge in this paper is 3D-Spine, soil-pile interaction is modeled by Kelvin-Voigt model and response spectrum method is applied to calculate its internal forces and modes to give some results of seismic response of cable stayed bridge. The results of the example show that when soil-structure interaction is taken into account, the internal forces of cable stayed bridge reduce significantly under an earthquake