The results of an experimental study of a ship rolling in irregular beam waves at zero speed are presented. The experiments were conducted in a wave tank using a 1:20 scale model of the fisheries protection vessel “Sulisker”. By digitally processing the roll response measurements, obtained over long periods of time, estimates of the probability distribution of the roll peak amplitudes were obtained and compared with some corresponding theoretical predictions. The theory was found to give good agreement with the experimental findings for four different wave elevation spectra. In particular, the experimentally observed deviation from the Rayleigh distribution, at high peak amplitudes, was correctly predicted by the theory. This deviation is largely attributable to the pronounced non-linear character of the roll damping.