Abstract: Considering the complexity of time history analysis on each curved bridge pier whose maximum response relies on the seismic angle, a relationship between the curvature at the bottom of the pier and the seismic response was presented based on the principle of Pushover method. The formula to calculate the critical angle was gained with non-liner Pushover method. Through the ease of a curved bridge, the critical angle to the seismic response of the curved bridge was calculated with the non-linear statically analytical method. The results of dynamical time history analysis in the range from 0° to 180° indicate that the formula is accurate to determine the critical angle to the seismic response of curved bridges.