||Sloshing waves induced by long-period components of earthquake ground motions may generate high magnitude hydrodynamic forces on liquid storage tanks. Past earthquake experience has shown that the forces generated by the sloshing waves may affect the overall safety of tanks by causing extensive damage on the tank wall and roof. Therefore, the accurate description of these forces is vital for reducing the potential risk of tank failure during an earthquake. Appropriate numerical simulation methods can be used to predict response of liquid storage tanks, as they offer a concise way of accurate consideration of all nonlinearities associated with fluid, tank and soil response in the same model. This chapter is, therefore, devoted to the Finite Element (FE) analysis of the sloshing phenomenon occurring in liquid storage tanks under external excitations. The governing equations for the fluid and structure and their solution methodologies are clarified. Current nonlinear FE modelling strategies for interactions between liquid, tank and soil are presented in great detail. The presented numerical modelling schemes are applied to analyze sloshing response of rectangular and cylindrical tanks when subjected to external excitations. Strong correlation between experimental and numerical results is obtained in terms of sloshing wave height for a rectangular tank model under resonant harmonic motion. Numerical simulations on cylindrical tanks have indicated that tank material, boundary conditions at the base and the presence of a second horizontal component in addition to one horizontal component have negligible effect on the sloshing response of cylindrical tanks when subjected to earthquake motions.