This paper investigates modifications to the dynamics of a marine vehicle caused by a point of inflection in its hydrostatic righting moment curve. Such inflections are shown to yield multiple equilibrium angles due to static over turning moments and to the occurrence of a classical fold catastrophe. Both frequency domain analyses and numerical solutions of the equation of roll motion are used to evaluate the influence of such inflections on the vessel’s dynamics. The analyses demonstrate that inflectional righting moment curves can yield unexpected roll amplitude jump phenomena close to resonance. The paper concludes with a discussion of the effects of such behavior on vessel hull designs.