Hugoniot relations of a two-dimensional axial shock with current and magnetic field in a cylindrical shock tube were investigated by a numerical method. The radial profiles of the magnetic field, electric current, pressures, flow velocities and temperatures between the up- and down-stream radial force-balanced plasma of the shock were revealed by numerical analysis. It is clearly found that the axial shock can lead to two effects： one is an inverse skin effect （i.e., the current density rises towards the center of the conductor）, the another is a reversed current effect which occurs near the edge and about a half radius. It is also found that the radial gradient of pressure, density and temperature all become very large near the center due to the axial shock.
