The concept of the surface impedance is applicable to the case, when obstacles on the surface of a vacuum chamber are small compared to characteristic dimensions of the problem. We apply this concept to the calculation of a synchronous mode that can propagate in a tube with slightly corrugated walls. We also show that such a mode can propagate in a pipe with a rough surface, or a perforated pipe with a large number of holes. ©1999 American Institute of Physics.