This study presents a theoretical method for calculating probabilities of capsizing due to pure loss of stability for a ship running in short crested waves and fluctuating wind. The aim was to develop stability criteria of a ship in quartering seas making use of the risk analysis. We divide the ship motions into the stationary motions and the unstationary motions. Then we integrate the probability density function, which is given by the stationary random process theory, on the safe domain that is determined by separatorices of the unstationary dynamical system. The reduction of restoring moment when a wave crest moves into the center of gravity of the ship is fully considered by Grim's effective wave concept. Numerical examples for a coastal trawler indicate that the probability of capsizing in quartering seas is larger than that in following or beam seas when the wind velocity is 10 m/sec. However, they also indicate that the probability of capsizing in beam seas is larger than that in following or quartering seas when the wind velocity is 20 m/sec. Furthermore, we concluded that the present method is effective for developing stability criteria, because the capsizing probabilities predicted by the present method are slightly larger than those given by the Monte Carlo simulation in time domain.