In order to study the effect of grain size on void formation during high-energy electron irradiations, the steady-state point defect concentration and vacancy supersaturation profiles have been calculated for three-dimensional spherical grains up to three microns in size. In the calculations of vacancy supersaturation as a function of grain size, the effects of internal sink density and the dislocation preference for interstitial attraction have been included. The computations show that the level of vacancy supersaturation achieved in a grain decreases with decreasing grain size. The grain size dependence of the maximum vacancy supersaturation in the centre of the grains is found to be very similar to the grain size dependence of the maximum void number density and void volume swelling measured in the central regions of austenitic stainless steel grains. This agreement reinforces the interpretation that the grain size effect is due primarily to the depletion of point defects from the grain interior. It is suggested that the void nucleation is strongly dependent on the level of vacancy supersaturation.