Resonant lining is an effective measure to reduce tonal noise in ducts. It has been observed that a fluid flow in the duct can interact with the lining in such a way that sound is amplified. A model for the acoustic performance of an infinite duct with periodic lining (quarter wavelength resonators) and a nonzero mean velocity is developed. The fluid in the duct and lining are separated by an infinitely thin shear layer, the velocity in the duct is uniform, and the velocity in the lining is zero. Such a layer is unstable for all frequencies, a so-called Helmholtz' instability. The linear acoustic equations are assumed to be valid. Based on the building block method, the acoustic modes in the periodic structure are calculated from the duct modes and scattering effects of the sharp edges. Numerical computations are done for a number of cases, where higher-order, evanescent, acoustic Floquet modes are omitted in order to simplify calculations. The direction of propagation of the computed modes is determined by the requirement of causality.