Space-charge impedance calculations for smooth vacuum chambers with an arbitrary cross-section and perfectly conducting walls are considered in the long-wavelength approximation, when&ohgr;b/(&bgr;&ggr;c)≪1,wherebis a typical transverse size. For the SNS beam energies&bgr;&ggr;⩽1.8,and the wavelengths are long when&lgr;≫b.Within the long-wavelength approximation, the fields can be found by solving a 2-D electrostatic problem. Two examples are presented: the space-charge impedance of screening wires (RF-cage) and of a ceramic chamber with inner metal stripes. In addition, we explore the transverse space-charge impedance of a circular pipe with account of betatron oscillations in a wide frequency range. ©1999 American Institute of Physics.