Two dimensional sloshing phenomena in regularly excited liquid cargo tank are numerically simulated with finite difference method. Navier-Stokes equations and continuity equation are computed for this study. The free-surface is determined every time step satisfying kinematic boundary condition using marker-density method. And the exciting force is treated by adding the acceleration of the tank to source term. The results are compared with other existing experiment results. And the comparison results show a good agreement. The sloshing phenomena in the tank of the 138K LNG carrier in sway motion is simulated with present calculation methods in low filling level. To find the relations between impact pressure and excitation condition, the calculations are performed in various amplitudes and periods. The averaged maximum pressures are compared each other.