A computer simulation of lattice distortions around an impurity ion Eu2+ in MeF2 fluorites (Me=Ca, Sr, Ba) is reported. ENDOR data on displacements of F- ions distant from an impurity center were used to determine the parameters of the Eu2+-F- short-range interaction potential. A theoretical study of the effect of hydrostatic pressure on the impurity-center local structure has been made. A comparison with experimental data permits a conclusion that the calculated ligand displacements are reliable. An experimental ENDOR investigation of the ligand hyperfine interaction (LHFI) in MeF2:Gd3+ crystals (Me=Ca, Sr, Pb, Ba) has been performed. The results obtained in the simulation are used to describe the LHFI of impurity ions with the nearest-neighbor fluorine environment. The contributions to LHFI associated with ligand polarization are shown to constitute 10-50% of the experimental LHFI constants. The inclusion of such contributions results in practically linear dependences of the remaining short-range part of the LHFI on distance.