Simulation techniques and a Volterra functional polynomial are applied as two alternative methods of calculating ship roll response to irregular waves. The roll motion is modeled by a single degree of freedom differential equation, with two alternative nonlinear damping functions. Estimation techniques are developed to obtain the coefficients of the damping functions from decay tests and from forced rolling tests. A linear plus quadratic form of damping function is found to be slightly preferable to a linear plus cubic form. The roll response process is found to be non-Gaussian, and characterised by negative values of the coefficient of kurtosis. Simulation results agree well with results obtained from the functional polynomial for low response levels, but show increasing disagreement as the response level increases, due to divergence of the functional polynomial representation. Analyses of results from model tests in irregular waves and from sea trials confirm the non-Gaussian nature of the roll response. A "constrained" form of the generalised gamma distribution function is found to provide an improved fit to the roll maxima and tothe roll minima, as compared to the Rayleigh distribution. The model tests also show some asymmetry in the roll response, which is not predicted by the theoretical model. It is suggested that this asymmetry may primarily be due to the combined effect of horizontal drift forces and the restraining system used to keep the model on station.