The Herschel-Quincke (HQ) tubes, consisting in putting tubes in derivation along a main acoustic wave guide, are used as passive devices to control fan noise. In order to assess the efficiency of this system, a new mixed analytical-numerical model is presented. The technique relies on combining Finite Element techniques to accurately describe the HQ tube with an integral representation for the acoustic pressure in the main duct. The presence of acoustic liners on the walls of the duct is taken into account via an appropriate modal decomposition of the Green's function. We show that our algorithm allows a very fast and accurate computation of the scattering matrix of such a system with a numerical complexity that grows very mildly with the frequency. Results show that ‘nearly' optimal configurations can be quickly identified with a very small computational expense.