An antiplane crack in a nonhomogeneous material is studied by assuming a continuously varying shear modulus which characterizes a decreasing rigidity near the crack tip. Explicit expressions for the stress and displacement fields are obtained and the influence of material softening upon these quantities is deduced. Depending upon the manner in which the rigidity decreases, the crack tip stresses may exhibit algebraic or logarithmic singularities or be bounded. In all instances the level of stress is less than that for a homogeneous medium and the crack profile is blunted. The relationship of material inhomogeneity to the notions of damage and a process zone is discussed and the implications of the results with regard to crack propagation are pointed out.