In this paper the acoustic absorption due to an orifice plate in a duct supporting a mean flow is studied theoretically. Absorption takes place as the acoustic field energizes a vortex field which is generated at the orifice rim. A linearized approximation is made to the absorption mechanism. This work presents an analytical extension of Howe [Proc. R. Soc. London, Ser. A366, 205–233 (1979)]. The latter deals with unsteady high Reynolds number flow through a circular aperture in a thin infinite screen. To the author’s knowledge, such an extension has not been previously made. The problem is formulated analytically insofar as it is possible and numerical results are presented. A Green’s function series expansion is used in the formulation. A difficulty arises with the convergence of this expansion. It is solved by a renormalization technique, which has been developed for this problem. The technique appears to be a novel method for dealing with convergence problems associated with term by term differentiation of Green’s function series expansions. To provide a check on the solution, it is shown that when the radius of the duct tends to infinity the present expression for the Rayleigh conductivity of the orifice plate limits to the expression obtained by Howe for an aperture in a thin infinite screen. With respect to the numerical results, it appears that for orifice mean flow Mach numbers≲0.2,an orifice to duct open area ratio of 0.3 provides near optimal average absorption, for the band of frequencies limited by the first symmetric mode cutoff frequency.