To investigate the impact of foundation settlement in loess areas on the dynamic response of liquid storage structure (LSS) under seismic motion, a finite element analysis model of the liquid–solid coupling of LSS was established using ADINA V9.6 software. By analyzing the dynamic response patterns of LSS under seismic motion with foundation failure, this study examines the effects of foundation failure and the direction of seismic wave incidence on the equivalent stress, maximum shear stress, wall displacement, and liquid sloshing wave height of the structure. The results indicate that among the three foundation failure scenarios, foundation failure at the center of the tank bottom has the least impact on the structural dynamic response. In contrast, foundation failure affecting one-fourth of the tank base has the greatest impact. Furthermore, compared to seismic motion along the X-axis, the dynamic response of the structure is more significantly affected when seismic motion co-occurs along the X-Z-axis.