The stability of electric arc discharges has been explored through the use of an energy balance coupled with charge conservation. In order to facilitate this analysis, a new model for the electrical conductivity function has been proposed. Asymptotic solutions for the arc governing equations have been obtained. Stability criteria have been developed from both the linear theory (infinitesimal size disturbance) and from a minimizing solution point of view for finite size disturbances. The results delineate an open region in the stability diagram where arc instabilities may be possible.