Experimental and theoretical studies of arc cathode region have been made during several decades and the task is not yet completed, in spite of many efforts and progress. In this work, a numerical model describing the arc cathode region is developed and applied for copper cathode at low current (4-50A). The model yields the temperature and electric field strength at the cathode surface, electrons emitted and total current density, cathode spot radius, different kinds of power densities heating and cooling the cathode, and the plasma electron density. The comparison with experimental results shows good agreement.