The structural and vibrational properties of the ZnO wurtzite phase with oxygen vacancies in different charged states are studied using first-principles and potential-based methods. The calculations based on density-functional theory are performed to determine the atomic configurations around defects. The DFT results are discussed and compared with those obtained using the static lattice method in the traditional shell model. Both computational approaches predict the same character of crystal lattice relaxation around oxygen vacancies. The phonon local symmetrized densities of states are calculated using the Green function method. The frequencies of localized vibrations of various symmetry types induced by oxygen vacancies in neutral and positively charged states are determined. The calculation results allow estimating the effect of oxygen vacancies on the formation of the intense Raman peak.