The effects of the biaxial compressive strain on the atomic relaxation and the formation energy of a neutral vacancy in Ge were investigated using first-principles calculations. Prior to this, the effects of the supercell size and Brillouin zone sampling were tested. The vacancy formation energy and atomic configuration around a vacancy are strongly affected by the inter-vacancy distance determined by the supercell size, due to the periodic boundary condition. The biaxial compressive strain reduced the formation energy of the vacancy nearly linearly by up to 1.34 eV as the magnitude of the biaxial compressive strain increased to the "Ge on Si (GoS)" condition. This was explained in terms of the bond strength characterized by the spatial electron density. The behavior of the vacancy in Ge was also compared with that in Si. (C) 2010 Elsevier B.V. All rights reserved.