The aim of this study is to present a Lyapunov function which can be used to derive an intact stability criterion for a ship in random beam seas. First, the mathematical model of the rolling motion of ships in random beam seas is introduced. The random wave excitation is described by a spectrum which is depended on the wave energy spectrum and the amplitude of the moment of roll. This spectrum is generated by a second order linear filter. Second, the methodology of creating a Lyapunov function is explained briefly. Then, there is outlined the way by which Lyapunov function can be used as the intact stability criterion for a ship. The proposed criterion is derived by considering the weather criteria for German naval vessels. Finally, the coherence of the boundary of safe basin obtained by Lyapunov function with the numerical results obtained by Euler-Maruyama Method is presented. From the results it can be deduced that the Lyapunov function can be used to define an intact stability criterion.