By using the complete energy matrix and taking into account the contributions from the spin orbit coupling of the central ions as well as those of the ligand ions, the local structure distortion have been studied for Cr3+ ions doping in KAl( MoO4), Y3Ga5O12, Y3Al5O12 and ZnAl2O4 crystals. The results show that the local structure exhibit elongation distortions for the doped systems. Moreover, the influence of the local structure parameter h on the EPR parameter D are studied. The relationships between D and (zeta, zeta') as well as the average parameter zeta(1) (zeta(1) = (zeta + zeta')/2) and the different parameter zeta(2) (zeta(2) = (zeta - zeta')/2) are discussed. (C) 2010 Elsevier B.V. All rights reserved.