Electrostatic shock waves are proposed as a possible mechanism for energizing electrons which are responsible for discrete auroras. It is shown that electrostatic shock solutions can exist in a Ti≫Te plasma carrying a field-aligned electron current if the plasma in the high-latitude plasma sheet has an earthward flow component. The model is formulated within the framework of the Vlasov-Poisson equations. The reflection of incident ions upstream, the trapping of electrons downstream, and the magentic mirror of the earth's field are included in the present model. It is found that under the high-latitude plasma sheet conditions, a field-aligned potential jump of several kilovolts can be produced by the shock. Electrons passing through the shock are accelerated at the expense of the ion kinetic energy.