A three-dimensional description of an axisymmetric unipolar arc discharge is given. Both sheath and plasma ball effects are taken into account. The analysis is based on the simultaneous solution of Ohm's law, Maxwell equations, and the boundary conditions for the electric potential at the plasma-sheath interface. These boundary conditions are dictated by the sheath effects. The potential distribution, current distribution, and magnetic fields in the plasma have been determined for a given electron density profile. These calculations show that the unipolar arc arises as a natural consequence of the pressure force.