When modeling planar discontinuities in acoustic waveguides at low frequencies, the standard assumptions involve continuity of pressure and volume velocity at the discontinuity. While continuity of volume velocity is required by mass conservation, excitation of evanescent higher‐order modes and thermoviscous loss suggest that pressure is not continuous across the discontinuity. Such a pressure loss can be modeled by a series acoustic impedance. A new model for a lumped series impedance at a planar waveguide discontinuity has been developed and is presented. The model uses a modal expansion of the acoustic field near the discontinuity and matrix techniques to obtain a closed‐form approximation for the resistive and reactive elements of the series impedance. As an example of the accuracy of the model, the prediction of the resonance frequency of a constricted annular resonator is presented. [This work was supported by the Office of Naval Research and the American Society of Engineering Education.]