One of the techniques by which highly ionized plasmas can be generated in the laboratory makes use of strong, electromagnetically driven shock waves propagating into a cold gas. In this paper the phenomenon is analyzed as a one-dimensional single-fluid hydromagnetic problem, neglecting dissipation behind the wave. We hypothesize that the rarefaction wave remains attached to the front. In the limit of essentially complete ionization behind the front the problem can be solved analytically as long as the transverse magnetic field there remains small compared with the longitudinal field.