An abrupt change of cross section in a circular lossless duct is considered. The analysis includes a nonrigid wall at the interface of both parts of the duct. Whereas previous investigators used iterative algorithms to calculate the behavior of the discontinuity, here a straightforward method is developed which avoids any convergence problems. In particular, large discontinuities can also be examined even if an arbitrary number of higher wave modes can propagate. The solution is given in form of a scattering matrix. For the plane wave mode a simple equivalent circuit is derived. The results are compared to an approximate solution given by Karal [J. Acoust. Soc. Am.25, 327–334 (1953)] and to a measurement. At low frequencies all data agree excellently. Some scattering parameters for different cases (different size of discontinuities, different wall admittances, difference frequency ranges) are represented. It is demonstrated that the magnitude of certain scattering parameters can exceed unity, if the corresponding wave is evanescent.