This study deals with probabilities of surf-riding of a ship in irregular following seas to develop stability criteria against broaching-to. Because, the surf-riding is a prerequisite for the broaching-to to happen. The author presented a theoretical method to calculate probabilities of surf-riding for a ship self-propelled with constant revolution in irregular seas. This theory is based on an assumption that a spectrum of the waves is narrow-banded. Probabilities of the "surf-riding under any initial conditions" are calculated by means of joint density of local wave height and period because this surf-riding depends on only a wave that the ship is situated on. For probabilities of the "surf-riding under certain initial conditions", we must consider both the wave and the preceding motion of the ship by means of joint density of wave height, phase and those derivatives. Calculated results showed that the probabilities of the "surf-riding under certain initial conditions " are not so small. This means that the "surf-riding under certain initial conditions" does not occur in regular seas but does in irregular seas. In addition, the calculated results quantitatively confirmed that a reduction of propeller revolution is one of effective measures to prevent surf-riding.
