A relaxation method based on the time dependent energy balance equation is used to derive steady state characteristics of arcs taking account of energy transfer due to thermal conduction, emission and absorption of radiation. The method involves calculating the radiation flux density as a function of radius for a given temperature profile using an integral solution of the radiation transport equation. An alternative but slightly less efficient form of the relaxation method uses a similar integration procedure but calculates the average radiation intensity. The methods have been applied to calculate the characteristics of discharges in sodium vapor where radiation other than from the D lines has been neglected. Results are presented for a pressure of 250 torr giving (1) temperature profiles and radiation efficiency as a function of electric current, tube radius and wall temperature, (2) characteristic line profiles of the radiation, and (3) the E-I characteristics of the discharge for the tube radii of 3·5 and 5 mm for currents ranging from 2 to 10 amps.