Stress and displacement fields for a propagating crack in a functionally gradient material (FGM) which has shear modulus as $mu$=$mu$$\_$0/(1＋ζX) are derived. The equations of motion in FGM which is nonhomogeneous material are different from those of homogeneous material. The stress intensity factors in stress fields have influence on odd terms of γ$^$n/2-1/(n=1,3,5,...,) but stress at crack tip only retains term of γ$^$-1/2/, where the γ is a radius of cylindrical coordinates centered at crack tip. When the FGM constant ζ is zero or γ→0, the fields for FGM are almost same as the those for isotropic material.