A mathematical model is presented for numerical experiments to predict the behavior of ship in severe following seas. At first, numerical experiments are carried out to investigate the dangerous situation leading up to surf-riding and capsize of ships in severe following and quartering seas. Next, the critical Froude number stands for surf-riding of ships in severe following seas. Finally, the stable and unstable range of directional stability are computed for the ship with combined motion of sway, roll and yaw.