Experiments have been carried out in a cylindrical magnetic shock tube on the propagation of a shock wave into a fluid containing a uniform transverse magnetic field. Cylindrical shock waves in the Mach number range from 20 to 100 have been produced which are very stable and reproducible. Theory predicts basic differences between the case where the gas is initially highly conducting (pre-ionized) and the case where a gas-ionizing shock propagates into a cold gas. Good agreement between theory and experiment has been obtained for the gas ionizing shocks.