The nonlinear dynamic response of a jack-up structure under random wave loads is considered. For a simplified jack-up model, average behavior and variability in extreme forces and responses are found from simulation over many 6-h seastates. Weibull and Hermite analytical models of response extremes are also presented and evaluated. These models use shorter, less expensive simulations to estimate a limited number of response statistics, such as moments or parameters of the response peak distribution, and fit analytical models to estimate global extremes. Necessary simulation lengths are established both for direct simulation of extremes, and for analytical extreme models.