The local lattice distortions and the EPR parameters (anisotropic g factors and the hyperfine structure constants) for the orthorhombic Pt(3+) center in YAG are theoretically investigated from the perturbation formulas of these parameters for a 5d(7) ion in an orthorhombically elongated octahedron. The [ PtO(6)] (9-) cluster on Al(3+) site is found to experience the axial elongation of about 0.01 along Z axis, and the planar impurity-ligand bond lengths suffer the relative variation of about 0.11 along X and Y axes due to the Jahn-Teller effect. As a result, the above local lattice distortions produce significant orthorhombic deformation, whereas the original slight trigonal distortion of the host [ AlO(6)] (9-) octahedron is entirely depressed by the Jahn-Teller effect. The calculated EPR parameters based on the above lattice distortions show good agreement with the experimental data, and the local structure of the impurity center is also discussed.