A theoretical and experimental study of the influence of shear flow on the attenuation of sound in a lined duct is presented. Both upstream and downstream propagation are considered. Solutions of the linearized equations for acoustic‐wave propagation in flow, based upon both uniform and power‐law models of the mean‐flow profile, are compared with attenuation measurements in a duct having two opposite side walls lined with a porous fiberglas® blanket for a frequency‐geometry rangekδ⩽1 and midstream Mach numbersMl<0.2. Here,kis the plane wavenumber and δ is the aerodynamic boundary‐layer thickness. Both profile models yield results in close agreement with experiments at low frequencies,kδ<0.1. For intermediate and high frequencies, 0.1