The local structure and the EPR parameters (zero-field splitting D, g factors g ‖ and g ⊥ and hyperfine structure constants A ‖ and A⊥) ofMn 4+ in LiF:U:Mn crystal have theoretically been investigated by using the perturbation formulas of the EPR parameters for a 3d 3 ion in trigonally distorted octahedra. In this trigonal Mn 4+ center, three U 6+ ions locate on (1,1,0), (1,0,1) and (0,1,1) sites, each surrounded by six O 2− ions. Thus, the studied system is characterized as the Mn 4+ associated with one host F − triangle, one O 2− triangle and an additional equivalent F’ − triangle containing the three U 6+ ions, i.e. an [MnF 3 O 3 F’ 3 ] 8 − cluster. The central Mn 4+ impurity is found to shift towards the oxygen triangle along the C 3 (or ) axis by an amount ΔZ (≈ 0.29 Å) due to the strong electrostatic attraction between the Mn 4+ and the oxygen triangle (and also the additional equivalent F’ − triangle), which increases the trigonal distortion of the Mn 4+ center considerably. The calculated EPR parameters based on the above displacement ΔZ agree reasonably with the observed values.