In ray‐theory solutions of propagation problems, one often determines a geometric boundary between an ensonified region and a shadow zone. It is desirable to be able to investigate the diffraction of sound into the shadow zone by a method of comparative simplicity. It is shown that the pressure discontinuity and the discontinuity of the normal derivative of the pressure determine the densities of a distribution of dipoles and of simple sources, respectively, such that there is a mutual annihilation of the geometric wave discontinuities and the distribution singularities. The radiation from the distributions (into both the ensonified region and the shadow zone) can be obtained by ray theory or by approximate wave‐theoretic techniques. In the case of a classical problem (for a homogeneous medium), there was agreement between the results of the above method and the classical results.