Abstarct: The free surface liquid sloshing in tank for storing and transporting liquids, LNG, chemicals, water, etc. is very important. Due to the excition of a foreign agent such as earthquakes or sloshing waves of the sea, the phenomenon of free surface liquid occurs in these tank. Therefore, estimating the frequency of liquid sloshing in the tank, the hydrodynamic pressures on the tank wall, and the suitable analysis of the liquid behavior inside the tank are essential for the suitable design of liquid storage tanks. In the present thesis, free surface liquid sloshing was simulated in a rectangular tank under lateral excition, two-dimensional and three-dimensional using open-source software OpenFOAM. First, a tank without baffle was modeled and the parameters of the free surface height near the wall, the pressure applied to the wall at different frequency excition of the tank was numerically studied, It was observed that at the excitation frequency, equal to the first natural frequency of the tank, there is a lot of pressure that can destroy the structure into the tank, for numerical simulation of the incompressible two phase flow in the tank was used baxsed on the Volume Of Fluid (VOF) method. Then, to examine the effects of a vertical baffle on the wall pressure control, two vertical baffle with different heights were used. The results show that the vertical baffle effectively reduces wall pressure. In the next step, the elastic property of the tank was used to reduce the numerical error and the effects of elasticity on free surface liquid sloshing were used from the vertical elastic damper blade and the results were compared with rigid. To simulate a vertical elastic baffle, the Fluid Structure Interaction baxsed on the Arbitary Lagrangian and Eulerian method (ALE). The governing equations on the linear elastic solid region were considered baxsed on the Finite Volume method and we used the Laplace equation with variable diffusivity equation for the mesh motion in the fluid and solid interface.