Abstract: The stochastic chaotic motion and the threshold parameter value for ships onset chaotic motion in random beam waves are studied by the probability density function and the numerical method. The random differential equation of ships’ rolling motion is established with considering the nonlinear damping, nonlinear restoring moment and the white noise wave excitation. The random Melnikov mean-square criterion is used to determine the threshold parameters for the ships’ stochastic chaotic motion. The probability density function of the rolling response is calculated through solving the stochastic differential equations by the path integral method. It is found that the ships undergo stochastic chaotic motion when the real intensity of the white noise exceeds the threshold value. For high intensity of white noise excitation, the stable probability density function has two peaks and the response of the system may jump from one high probability state to another. That will lead ships to instability and even to capsizing.