A theoretical description of local relaxation effects-induced by the presence of impurity centers V4+ at the tetrahedral and dodecahedral sites of ZrSiO4 is presented. The crystal structure is analyzed via optimization of local equilibrium : geometries and computation of the force constant associated with the symmetric vibrational mode at each impurity center. The theoretical study is carried but using an extension of the ab initio perturbed ion method. The relative stability of vanadium-substituted vacancies in ZrSiO4 is examined in light of previous results reported by the present authors and the vibrational analysis here addressed. Local geometries were optimized by relaxing various sets of ions around each substituted center. An increased substitution energy together with a pronounced decrease of the breathing vibrational mode on the 4-fold-coordinated site shows that this substitution is unstable while that on the 8-fold-coordinated ion site is energetically favorable and the local geometry is minimally relaxed. Selective doping on each center leads to a decreased force constant as compared to that obtained for the pure crystal structure.