A computer controlled ENDOR spectrometer and special software are used to determine the coordinates of 19F nuclei in four anionic spheres of cubic MeF2:Gd3+ (Me = Ca, Sr, Ba, Pb) centers. The computer simulation of Gd3+ cubic impurity center in crystals MeF2 (Me = Ca, Sr, Ba) has been also performed. The analysis of lattice relaxation near the impurity center carried out on the base of ENDOR experiments data has allowed us to obtain potential of interaction Gd3+-F-. For the first time not only radial displacements but also angular displacements of F- ions of the third sphere have been taken into account and it has been shown that it influences the determination of lattice relaxation around the impurity center essentially. The influence of hydrostatic pressure (up to 30 kbar) on the local structure of the impurity center has also been investigated using computer simulation. The comparison of the experimental and calculated displacements of distant ions gives a reliable test of the validity of theoretical lattice relaxation model and accuracy of calculations of impurity-directed shifts of ligands.