An exact solution of the antiplane problem for a semi-infinite interface crack in a piecewise-homogeneous wedge under a self-balanced load on its sides has been obtained. Three types of boundary conditions on the wedge sides were examined: the both sides being stress-free; both sides being clamped, and one side being stress-free with the second one clamped. As a result of using the Wiener-Hopf method, the solution was represented in quadratures. The Green’s functions were obtained for stress intensity factors; in the case of a geometrically symmetrical wedge structure simple formulae were found for these functions. The stress singularity in the apex of the wedge was studied. In contrast to the homogeneous wedge structure the asymptotic of the stresses near the apex was established to have sometimes two singular terms for some values of the composite parameters.