In this article we present the exact solution, to first order of the interacting field, of the following canonical problem. We consider the scattering system consisting of an isotropic elastic medium containing an infinite cylindrical void (= hole), from which emanates a half-penny-shaped crack. The crack lies in a plane containing the axis of the cylindrical void, also the crack intersects the void at its own axis of symmetry. In the paragraph below we define what is meant by obtaining the solution ‘to first order’.