Parametric roll may be defined as the spontaneous rolling motion of the ship moving in head or following seas that comes about as a result of the dynamic instability of motion. The development of the parametric roll occurs under the conditions that the encounter angular frequency is approximately twice the roll angular frequency, the wavelength is equal to the ship length and the roll damping is insufficient to dissipate the parametric roll energy. In this Thesis the dynamic roll behaviour for 5 different combinations of wave heights and wavelengths for different initial conditions and different initial wave positions, without and with a realistic amount of damping have been studied. The Methods used are the three Equations of roll motion based on three variants of the stiffness term in the basic Mathieu equation with damping.