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Stress and displacement fields of a propagating Mode III crack in an orthotropic functionally gradient material (OFGM), which has (1) linear variation of shear modulus with a constant density, and (2) an exponential variation of shear modulus and density, are derived. The equations of motion in OFGM are developed and solution to the displacement and stress fields for a propagating crack at constant speed though an asymptotic analysis. The stress terms associated with and are not affected by the FGM constant which is nonhomogeneous parameter, only on the higher order terms, the influences of nonhomogeneity on the stress are explicitly brought out. When the FGM constant is zero or 0, the fields for OFGM are almost same as the those for homogeneous orthotropic material. Using the stress components, the effects of nonhomogeneity on stress components are discussed.