The investigation by Pridmore‐Brown of the effects of shear on the downstream propagation of sound in rigid‐walled rectangular ducts has been extended to include upstream sound propagation as well as the effects of boundary‐layer thickness. Solutions are given in terms of a combined Galerkin‐Runge‐Kutta numerical technique as well as in terms of a technique based upon a perturbation of the well‐known zero Mach number solution. The effect of shear on upstream sound propagation is to refract the sound into the center of the duct. The effect of refraction is found to be important for boundary‐layer flows when the ratio of boundary‐layer height to acoustic wavelength is equal to or greater than unity.