The idealised equilibrium profile is thought of as one in which the beach profile and sediment grain size distribution across the profile are in equilibrium with the wave-generated hydraulic regime. Field observations of a seaward-fining gradient suggest that sediment of a particular size may move across the profile to a position in which it is in equilibrium with the wave and flows acting on that sediment grain. Two major hypotheses have been proposed to explain the selective shore-normal sorting of grain sizes: the hypothesis of asymmetrical thresholds under waves, and the null-point hypothesis. Although neither of these hypotheses has been fully accepted, neither has been unequivocally rejected. The null-point hypothesis is still a central point of discussion in most studies of beach equilibrium, and the idea of an equilibrium sediment size gradient has not been abandoned. The predictions of a numerical model developed to test the hypothesis of asymmetrical thresholds under waves are compared to measured sediment size variations on five beaches. The model is more successful at predicting the general trend of onshore sediment size increase than at predicting actual sediment sizes. The results of this research indicate that a mean sediment size cannot be related simply to wave-induced velocities, and suggest that further exploration of a threshold or equilibrium hypothesis will not provide a great deal more insight into the processes responsible for sediment sorting.