In this paper, the axisymmetric crack problem for a nonhomogeneous medium is considered. It is assumed that the shear modulus is a function of z approximated by μ = μ0 eαz . This is a simple simulation of materials and interfacial zones with intentionally or naturally graded properties. The problem is a mixed-mode problem and is formualated in terms of a pair of singular integral equations. With fracture mechanics applications in mind, the main results given are the stress intensity factors as a function of the nonhomogeneity parameter a for various loading conditions. Also given are some sample results showing the crack opening displacements.