The diffusion of vacancies in Ge and Si during quenching from the melting point is examined mathematically. In typical dendrites of either material (0.01‐cm‐thick ribbons), cooling after growth is slow enough so that only 10−3of the concentration of vacancies at the melting point &phgr;0can be trapped. For this calculation vacancies are considered as the only defects present, and surfaces are considered as the only vacancy sinks. For Ge samples of larger dimensions (approximately 0.1 cm) cooled by radiation alone the concentration trapped can be34[open phi]0with surfaces acting as the only sinks. However, if dislocations in excess of 104per cm2are present acting as vacancy sinks of 10−7‐cm radius, the concentration quenched‐in drops very rapidly with increasing dislocation density. At 105per cm2only 10−2&phgr;0are quenched‐in. Thus, if samples contain more than 105dislocations per cm2, vacancies would probably not be observed in radiation quenching experiments. Existing theory combined with the present calculation indicates that the formation of dislocation loops in growing Ge dendrites is unlikely.