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In this work, acoustic performances of a liner concept based on perforated screens backed by air cavities are investigated numerically for circular ducts with mean flow. Dimensions of the cavity are chosen to be of the order or bigger than the wavelength so acoustic waves within the liner can propagate parallel to the duct surface. In this case, the liner becomes nonlocally reacting and this gives rise to additional resonance effects which renders the attenuation more effective over a broader frequency range. In order to predict the mufflers’ acoustic performances, a special boundary integral method is presented. Using a tailored Green’s function for hard wall circular ducts containing uniform mean flow, the numerical technique only requires the discretization of the acoustic velocity potential on both sides of the perforated screen separating the central channel from the air cavities. Comparisons with finite element results show that the proposed method allows accurate results for a relatively modest computational cost. Influence of the mean flow in the central airway, the dimensions of the cavity as well as the nature of the incident field on acoustic performances are also shown and discussed.