We studied a restoring force model that considers post-buckling and a new analytical method for calculating the dynamic behavior of silos in earthquakes. In order to improve rational seismic design, we analyzed vibration responses to various seismic waves. In addition, we investigated a new method for analyzing the vibration response by comparing the static restoring force model with those of the newly developed dynamic restoring force model. We also propose an analytical model for the equivalent mass of one degree of freedom before and after buckling for effective mass vibration of silos in earthquakes. In the future, the research on new analytical model (dynamic hysteresis model and equivalent mass model) will enable the calculation of the vibration responses and reliable structure's specific coefficients of silos.