This paper analyzes the free vibration and the response of geometrical non-linearity, material non-linearity and geometrical material coupled non-linearity of the Longtanhe bridge, which located in Zigui county, Hubei province. First, the characteristics of the concrete-filled with steel tube arch bridge and the survey of Longtanhe bridge are introduced, and a computational model of the space bar is built. Secondly, the properties of free vibration of Longtanhe bridge are analyzed. Finally, its characteristics of nonlinear seismic response are calculated by EI-Centro seismic wave and conclusions are reached, namely, though the effect of geometrical non-linearity is not obvious, that of material non-linearity and of geometrical material coupled non-linearity is very obvious in the resisting earthquake analysis of the concrete-filled with steel tube arch bridge in which span is not long.
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