This study investigates the roll motion of a ship with low metacentric height and significantly nonlinear restoring when the excitation is given by bi-chromatic and mono-chromatic beam waves. Experiments and simulations have been performed. Simulations are carried out by means of two different 1-DOF models, where roll restoring is modelled either using an absolute or a relative angle approach, and by means of a 6-DOF blended code. Large amplitude sub-harmonic rolling has been identified in experiments and by some of the numerical models. The capability of the mathematical models of reproducing the experimental behaviour is discussed.