The roll response of a ship to random beam seas is investigated in terms of the threshold crossing process. The non-white excitation process is modeled as an equivalent white-noise one based on the assumption that the upcrossing properties of the response can be approximately replaced by the excitation with a white noise process with a suitable intensity. Then the non-linear damping is reinstated. The reinstated equation of motion with the equivalent white-noise intensity is solved using the equivalent non-linear method to get the desired probability density function. The proposed scheme is tested extensively with varing coefficients.