Target equipment damage is a key factor in the quantitative risk assessment of domino effects caused by blast fragments. However, the damage process of target equipment caused by blast fragments in domino effect accidents has not been studied clearly. In this paper, a finite element (FE) model of large vertical storage tanks impacted by blast fragments is built to study the damage process. A small-scaled fragment impact experiment is carried out to validate the FE modeling approach. Based on accident statistical data and empirical formulas, the reasonable ranges of blast fragment parameters are obtained. The comparison between the rigid and the elastic–plastic fragment impact is conducted. The effects of filling degree, tank volume, impact height, roof-impact angle, fragment type, impact velocity and impact angle on the damage process are discussed. It can be concluded that: (1) The “added mass” effect of the inner liquid on the impact process increases with the filling degree. The fragment deformation has important effects on the impact process. (2) The impact process includes multiple collisions rather than only one collision. (3) The reduction of tank volume and the increase of impact height on tank wall can increase the damage degree. The impact on roof edge can make the fragment penetration easier. (4) End-caps for identical kinetic energy are more harmful to tanks than plates. The end-cap impact with horizontal impact angle of 35° causes the most serious deformation. This study provides insights into the damage mechanism and prevention of domino effects caused by blast fragments.