The transmission of sound in an acoustically treated circular duct containing sheared flow is treated by reduction of the governing equations to a two‐point boundary‐value problem. The pressure modes and transmission wavenumbers are obtained by an iterative procedure for a wide range of driving frequencies, duct‐flow Mach numbers, and boundary‐layer thicknesses with a given lining impedance model. Computations are made for both inlet and exhaust flows. For inlet flows, the direction of sound propagation is opposite to the flow direction, while in the exhaust flow the sound is propagated in the same direction as the flow. The numerical results show a major reduction of achievable attenuation of the least attenuated mode in the inlet flow, owing to the presence of the boundary layer, particularly at the higher Mach numbers. The attenuation in the exhaust flow shows only minor effects due to the presence of a boundary layer. The reduction in attenuation in the inlet flow indicates that the design of acoustic linings for inlet applications must include careful consideration of boundary‐layer effects.