The present study describes a numerical analysis for simulation of the sloshing of flows with free-surface which contained in a rectangular tank moving in harmonic or pitching motion. The VOF function, representing the volume fraction of a cell occupied by the fluid, is calculated for each cells, which gives the location of the free-surface filling any some fraction of cells with fluid. The time-dependent changes of free-surface height are used for visualization subject to several conditions such as fluid height, horizontal acceleration, sinusoidal motion, and viscosity. The free-surface heights were used for comparing wall-force, which is caused by sloshing of flows. Damping effects by baffles were extensively investigated for various conditions in terms of baffle shape and position.