Experimental observations teach us that the deck wetness does not necessarily occur repeatedly even in regular waves high enough to cause it when the wave period is close to the natural rolling period of the ship. The shipping water caused by the first one or two waves exceeding the critical wave height of deck wetness reduces GM, lengthens the natural rolling period to lead to the reduction of the rolling angle, and stops wet deck from occurring repeatedly. In order to understand the stability of ships in waves exceeding the 'critical wave height of deck wetness, we propose in this report a simplified time domain simulation to describe the ship motions from the start of deck wetness to the capsize or to the stationary oscillation around a heeling angle while taking into account above mentioned rather transient effects of shipping water. In the formulation of the time domain simulation, we use an empirical formula relating the amount of the water flowing onto deck, every time deck wetness occurs, to the excess of the predicted relative wave elevation over the bulwark-top. We compared the numerical simulations with the time histories of motions in experiments with the cylindrical models in beam seas, from the start of deck wetness to the capsize ; we thereby concluded that the numerical simulations describe that process well.