Propagation of magnetohydrodynamic waves is investigated in a fluid bounded by a cylindrical surface of constant, but not necessarily circular, cross section. The fluid is assumed to be nonviscous and perfectly conducting with a constant magnetic field applied parallel to the walls of the cylinder. It is shown that the following types of waves can propagate in such a wave guide: (1) transverse waves propagating without dispersion with the velocity of Alfve´n waves; (2) a longitudinal wave, identical with the wave of the principal mode for an acoustic wave guide; (3) waves having both longitudinal and transverse components propagating with a dispersion, their group and phase velocity being close to the respective velocities for an acoustic wave guide; (4) waves having both longitudinal and transverse components propagating with a small dispersion, their group and phase velocity being close to the velocity of Alfve´n waves. When the applied frequency is too low, damping of certain modes appears for waves of type (3), only; the cut‐off frequencies turn out to be slightly higher than the corresponding cut‐off frequencies for an acoustic wave guide.