The EPR parameters and fine spectra for Cr³⁺ ion in YAG crystal were studied by using two distortion models and complete diagonalization method(CDM). The investigations consider for the first time the spin-spin (SS) and spin-other-orbit (SOO) interactions. The studies show that the local structure in the YAG∶Cr³⁺ crystal is of the compressed trigonal distortion (Δθ=1.88°). Accordingly,the EPR parameters and fine spectra for Cr³⁺ ion in YAG crystal are explained successfully. By analyzing these models,it shows that the impurity ion moving model is not suitable if there are the same charge for the impurity ion and host ion. Since local structure is sensitive to both ground state zero field splitting (ZFS) and the first excited state ZFS,it is not reliable to decide local lattice distortion only using ground state ZFS parameter D.