In this work, global analysis of ship rolling motion as effected by parametric excitation is studied. The parametric excitation results from the roll restoring moment variation as a wave train passes. In addition to the parametric excitation, an external periodic wave excitation and steady wind bias are also included in the analysis. The roll motion is the most critical motion for a ship because of the possibility of capsizing. The boundaries in the Poincaré map which separate initial conditions which eventually evolve to bounded steady state solutions and those which lead to unbounded capsizing motion are studied. The changes in these boundaries or manifolds as effected by changes in the ship and environmental conditions are analyzed. The region in the Poincaré map which lead to bounded steady state motions is called the safe basin. The size of this safe basin is a measure of the vessel’s resistance to capsizing.