Abstract: The kinematics of the arbitrary Lagrangian-Eulerian(ALE) description is introduced and the fluid dynamics equations are revised in the ALE form. The numerical discrete equations of fractional steps finite element method are developed by streamline-upwind/Petrov-Galerkin formulation. In order to confirm the effectiveness of the method, large-amplitude liquid sloshing in a tank is simulated. The results are compared with those of previously proposed methods and available experimental results. Good agreement is obtained.