The two‐dimensional problem of the interaction of a hypersonic flow with the field of a current carrying wire is analyzed. The electrical conductivity behind the normal shock is taken to have an arbitrary finite value, while the free stream conductivity is zero. It is found that the magnetohydro‐dynamically supported shock wave follows the magnetic field lines closely and that the hot flow is confined to a narrow region behind the shock at all values of conductivity. For low conductivities the shock position is determined by setting the interaction parameter based on the velocity behind the normal shock and a distance of &egr; times the shock radius equal to ⅓[1 + (2&egr;)½] where &egr;(≪1) is the density ratio across the shock. The high conductivity case is reached when the magnetic Reynolds number, based on the above parameters, exceeds unity. The shock position is then determined by equating the dynamic and magnetic pressures. The thickness of the current sheet in this case is of the order of the shock radius divided byRm½&egr;−¾. For low conductivities the case of a wire embedded in a solid cylinder has also been considered, and it is shown that the heat transfer is reduced sharply when the shock wave is lifted off of the surface of the cylinder.