The steady-state electric-current distribution and the magnetic pressure in a uniform conducting medium, flowing in a cylindrical configuration between two circular electrodes, was determined by solving the magnetic field transport equation with a superimposed axial magnetic field. This medium models the interelectrode plasma of the diffuse mode metal vapor vacuum arc.The results show the following.a) The electric current and the flux of the poloidal magnetic field are constricted at the anode side of the flowing plasma. Most of the constriction takes place within a boundary layer, with a characteristic length of 1/Rme, where Rme is the magnetic-Reynolds number for axial electron flow. b) The electric-current constriction inversely depends on [formula omitted], where [formula omitted] is the azimuthal surface current density which produces the axial magnetic field. c) The magnetic-pressure profile shows a radial pinch force in most of the interelectrode region, but in the anode boundary layer it is axially directed, thus retarding the plasma flow.d) The peak of the magnetic pressure is at the anode, and its amplitude directly depends on [formula omitted]. As [formula omitted] increases, the peak location moves toward the anode center.