The effect of a vacancy on the lattice dynamics of a f.c.c. Born-von Kármánn lattice with nearest-neighbours interaction is studied on the basis of Lifschitz's theory to account for the local failure of interatomic bonds. The long range elastic relaxation is considered for the particular case of argon crystals in order to estimate, up to the first order, the change of thermodynamic vibrational properties. Both the perturbation matrix due to the vacancy in the unrelaxed lattice and the inverse matrix ( L − ω 2) -1, where L is the dynamic matrix and to is the vibrational frequency, are represented in terms of the symmetry co-ordinates pertaining to the set of atoms involved in the perturbation. No localized modes are found in the unrelaxed lattice. The vacancy entropy is studied here both at constant volume and at constant pressure. The entropy at constant volume, in the high temperature limit, is found to be ( ΔS) unrelax. V = 2·08 k in the unrelaxed lattice and ( ΔS) V relax = 2·74 k when the elastic relaxation around the vacancy is taken into account. The entropy at constant pressure is ( ΔS) P unrelax. = 4 k and ( ΔS) P relax. = 8.1 k, respectively, for Argon crystals at 80°K. The strong anharmonicity of argon crystals, as compared to metals, seems to be responsible for the surprisingly large difference between the constant volume and constant pressure entropies near the triple point temperature. A comparison is made between the theoretical value at constant pressure and the values deduced by Foreman and Lidiard from specific heat measurements in solid argon. Even if the calculated entropy is too high as compared with experimental data, the agreement is much better than with the previous theoretical estimate.