In industrial processes, the liquid slug trapped in pipes is one of the most important factors that affect the system safety. When the system is reactivated, propelled slugs will seriously impact elbows and cause serious accident in the pipe systems. Therefore, it is important to analyze the fluid-structure interaction of elbows under a transient liquid slug by numerical simulation. Based on the Arbitrary Lagrangian Eulerian (ALE) approach, the transient process was simulated by the FEA model effectively. Using the penalty coupling algorithm method, fluid-structure interaction (FSI) was successfully simulated. The coupling force changengover time was curved. Besides, the response of the elbow was also analyzed. The pressure distribution and dynamic stress in were recorded to find out the peak maximum stress. To confirm the region with high-stress level, the stress field was given in contour plot at the critical time. Furthermore, the potential damaged position was predicted in this transient process. Finally, the influence of the flow velocity was investigated in details.