Using the Green function method of lattice statics, the lattice distortion in the neighborhood of a vacancy in magnesium has been calculated in three different axially-symmetric (AS) host lattice models and also in a model derived from an empirical interatomic pair potential. The variations in the lattice distortion and the relaxation energy of the vacancy are studied as the size of the defect space is allowed to vary from two to four surrounding neighbors. The perfect static lattice Green functions are computed up to 19 neighbors in the 4 models and the values obtained are shown to be not very sensitive to the model chosen. The lattice relaxation is found to be negligible in all models except in a four-neighbor AS model. The relaxation energies in these four models are computed to be 0.0027 eV, 0.034 eV, 0.28 eV and 0.0069 eV respectively. Results for the monovacancy formation energy, the elastic dipole tensor and the volume change of the crystal due to the vacancy are also presented.