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Based on the superposition model, in this paper the EPR parameters g II  and g ⊥  of Dy 3+ , and the hyperfine structure constants A II  and A ⊥  of  161 Dy 3+  and  163 Dy 3+  in LuPO 4  crystal are calculated by perturbation formulas from the crystal-field theory. In the calculations, the contributions of various admixtures and interactions such as J-mixing, mixtures among states with the same J-value, twoorder perturbation, covalency as well as local lattice relaxation are considered. The calculated results agree reasonably with the observed values

Theoretical Interpretation of the EPR Parameters for Dy 3+ Ion in LuPO 4 Crystal