Abstract: In this work, two stability failure models, i.e., the dead ship condition and parametric roll are selected in order to study and evaluate ship stability as well as safety at seas. Specifically, equations are established to describe the roll motions under the dead ship condition and the parametric roll condition, respectively. Subsequently, equations of the roll motion are coupled with the linear filter, and the roll responses are obtained by solving the coupled equations via the Runge Kutta method. The stochastic process X(t) is defined as the absolute value of the roll response, and the average conditional exceedance rate (ACER) method is employed to predict the extreme value distribution of X(t). It is observed that the ACER method can provide satisfactory predictions of the extreme value distributions for the roll response under the dead ship condition and the parametric roll condition. The exceedance probability for the stochastic process X(t) at the critical level (e.g. the flooding angle), can be applied as an effective index to evaluate ship capsizing at seas. Extreme value analysis of the roll motion by application of the ACER method could be an important reference to evaluated ship stability at seas.