The stability of the shock front under free-flow down the expansion tube of an electromagnetically driven shock tube is investigated. The results of a wide range of experiments covering different electrode geometries, ambient gas pressures and front velocities in hydrogen, helium and argon are analysed. It is found that a condition for stability can be found in terms of a critical hydrodynamic Reynold's number of about 9000 for the flow. The implications of this result are discussed.