Abstract: The Lattice Bhatnager Gross Krook(LBGK) method combined with the large eddy turbulent model is applied to the numerical simulation of the viscous flow,and the Volume of fluid(VOF) concept is introduced into the LBGK method,which is used to simulate the action of the free surface The free sloshing of the viscous liquid in a tank as well as the first mode sloshing excited by the nonlinear acceleration are simulated.The pressure distribution at the wall of tank is obtained.The equations of pressure force and bending moment are fitted.Both the theoretical analysis and the simulation result show that themethod in the paper has high precision in the simulation of the incompressible flows with a free surface.