The local lattice structure and electron paramagnetic resonance (EPR) spectra have been studied systematically by diagonalizing 364×364 complete energy matrices for a f¹¹ ion in a trigonal ligand-field. By simulating the calculated Stark levels and EPR parameters to the experimental results, the shift parameters are determined for Er³⁺ ions in BaF₂ and SrF₂. The results show that the trigonal center is attributed to an interstitial F⁻ ion located at the [111] axis of the cube, and the nearest ligand close to the charge compensator has a displacement towards central ion by 0.042Å for L center in BaF₂:Er³⁺ and 0.026Å for J center in SrF₂:Er³⁺, respectively. Moreover, the relationships between g-factors and shift parameter ΔZ as well as orbit reduction factor k′ are discussed.