Unsteady, one‐dimensional magnetohydrodynamic shock formation in a shock tube has been studied by numerical solution of the single‐fluid continuum equations, using numerical dissipation as the only diffusion mechanism. The results are qualitative inasmuch as the exact shapes of the various profiles are not predicted. However, considerable physical insight has been gained, particularly concerning the early‐time evolution of the shock wave and its separation from the drive‐current layer. By appropriate scaling, these results can be compared with experiments, and are useful in their interpretation. Many of the departures of experimental results from ideal theory can be explained in terms of finite dissipation, without introducing anomalous effects.