A Green’s function extension of image theory allows the sound field in an absorbing fluid substrate underlying a fluid wedge of slower sound speed to be evaluated on a desktop computer. (1) Solutions based on an end‐point approximation, valid at great distances from the apex of the wedge and for absorptions representative of sedimentarylike materials, show a beam peaking at a depth close to that predicted by more complicated models. An additional random‐phase assumption provides a functional dependence for this angle identical with that obtained by a more elaborate procedure. (2) Solutions based on a saddle‐point approximation are valid below the apex and for arbitrary absorption. At moderate absorption, these solutions are consistent with those observed in the farfield. For small absorption, the sound field displays a heretofore unnoticed structure that is consistent with the mutual interference of sound beams entering the substrate at various distances from the apex. Some previously unreported measurements of the sound field in the substrate support the predictions of the saddle‐point approximation.