The self-consistent calculations of the spatial distributions of electrons and potentials in vacancies of metals with a localized positron, the spatial distributions of positrons localized in surface states, and the binding energies of positrons and their lifetimes have been performed in terms of the Kohn-Sham method and the stabilized jellium model. The presence of a localized positron in a vacancy leads to the effect that the vacancy is weakly distinguishable for electron waves: the positron weakens the potential field in the vicinity of the vacancy and leads to a phase shift of the scattering electron wave functions. The calculation of the phase shifts of the wave functions for quasi-free positrons scattered by unperturbed vacancies and the representation of a system of vacancies as a “superlattice” in a metal have made it possible to find the shift of the positron work function and the vacancy contribution to the positron effective mass.