A detailed calculation is given of the effect of an impurity atmosphere on void growth under irradiation damage conditions. Norris has proposed that such an atmosphere can suppress void growth. We have found the hydrostatic stress field of a dislocation that is surrounded by an impurity atmosphere and from it have calculated the change in the effective radius of a dislocation line as a sink for interstitials and vacancies. The calculation of the impurity concentration in a Cottrell cloud takes into account the change in hydrostatic pressure produced by the presence of the cloud itself. It is assumed that the hydrostatic pressure field of an impurity atom exists over a radial distance larger than the radius of the impurity atom. It is found that void growth is eliminated whenever dislocations are surrounded by a condensed atmosphere of either oversized substitutional impurity atoms or interstitial impurity atoms. A condensed atmosphere will form whenever the average impurity concentration is larger than a critical concentration.