The errors of a ray‐theory solution of simple harmonic acoustic propagation in an inhomogeneous medium are shown to be corrected by radiation from a distribution of simple source whose density has the phase of the incident ray amplitude. In the case of singularities in the ray field, the density involves symbolic functions. The radiation from the distributed sources is obtained by iterative ray techniques based either on a Green's function formulation or an integral equation. An alternative technique uses an iterated artificial wavenumber. In an example, the modified ray‐theoretic solution for lateral waves is given.