The earthquake safety of large storage tanks is a matter of great concern today. In this study, we used ANSYS software to establish a finite element model of the tank-liquid coupled system and consider the nonlinear contact effect between the tank bottom and foundation. We selected the El-Centro earthquake wave in the north-south and vertical directions, which is typically selected as input, for our analysis of the tank-liquid coupled system. Then, we investigated the seismic response of the storage tank in two cases-under horizontal earthquake excitation and under simultaneous horizontal and vertical earthquake excitation. Our study results show elephant-foot deformation to occur within 1.2 m of the tank wall bottom, which produces a larger relative horizontal displacement in the tank wall bottom in the case with simultaneous horizontal and vertical earthquake excitation. In addition, we observed there to be some influence on the hoop stress, axial compressive stress on the tank wall, and base shear of different degrees under simultaneous horizontal and vertical earthquake excitation, but little effect on the vertical shaking of the liquid. We observed some obvious nonlinear uplift and permanent slippage at the tank wall bottom under the simultaneous horizontal and vertical earthquake excitation. The influence of vertical excitation on the tank response is unfavorable and cannot be ignored. Thus, the seismic design of storage tanks should consider the impact of vertical seismic-wave excitation. These research conclusions provide a reference and basis for the future seismic design of vertical storage tanks.