Abstract In this paper, stress distribution in a compound disk or compound cylinder, embedded an edge dislocation is determined through an exact formulation of the plane elasticity problem. The dislocation solution is then used as a Green's function to approach general compound disk crack problems. By superposition and integration of the dislocation solution, the stress intensity factors of the crack can be formulated in terms of a singular integral equation, and evaluated using a collocation technique accurately. As an example, numerical results of stress intensity factors for a radial crack in a compound disk subjected to uniform crack surface pressure are given. Effects of disk-annulus geometries and stiffness on the crack behavior are studied. Various special cases are also discussed and compared with existing solutions.