The arbitrary Lagrange-Eulerian (ALE) finite element method (FEM) was successfully used to analyze fluid-structure interaction with a free surface. The fluid was regarded as a convection dominated incompressible viscous with the viscous and the slip boundary conditions. Generalized variational principles were established for the problem with large amplitude sloshing due to the free fluid surface. The Newmark-β integration method with a predictor-corrector scheme was used to solve the nonlinear dynamic response of the coupled ALE-FEM equations. Numerical examples were given to analyze the effects of a tuned liquid damper (TLD) setting on the structure. The horizontal nonlinear displacement responses in time domain at the top of the structure and the fluid elevation histories along the wall were computed and compared with predictions of a simplified mass-spring system. The arbitrary Lagrange-Eulerian (ALE) finite element method (FEM) was successfully used to analyze fluid-structure interaction with a free surface. The fluid was considered as a convection dominated incompressible viscous with the viscous and the slip boundary conditions. Generalized variational principles were established for the problem with large amplitude sloshing due to the free fluid surface. The Newmark-β integration method with a predictor-corrector scheme was used to solve the nonlinear dynamic response of the coupled ALE-FEM equations. the effects of a tuned liquid damper (TLD) setting on the structure. The horizontal nonlinear displacement responses in time domain at the top of the structure and the fluid elevation histories along the wall were computed and compared with predictions of a simplified mass-spring system .