Results of computer simulations of the water motion in ship anti-roll tanks are compared with experimental data. The numerical computations are done with a Volume Of Fluid (VOF) based NavierStokes solver. Both free-surface anti-roll tanks and U-tube anti-roll tanks are considered. Calculated and measured results for the local wave heights, the sway force and roll moment are presented for both regular and irregular tank motions. A simple but effective simulation model for the active control of U-tube anti-roll tanks is introduced. Finally, the fully nonlinear time-domain coupling of the ship motion and the tank water motion is established.