Performance evaluation of electricity distribution units is an important issue between researchers and regulators. Classic Data Envelopment Analysis models with deterministic data have been used by many authors to measure efficiency of power distribution units in different countries. However, Data Envelopment Analysis with stochastic data are rarely used to measure efficiency of distribution companies. In this paper, input oriented model in stochastic Data Envelopment Analysis is used to evaluate power distribution units in Iran. In addition, variable returns to scale super efficiency model is used in stochastic Data Envelopment Analysis to rank stochastic efficient units. Deterministic equivalent of each stochastic model, which can be converted to a quadratic program, is applied to obtain numerical results with stochastic data. Under fairly general conditions, this model equivalent program is replaced by a linear programming problem. 38 Iranian electricity distribution units have been considered in this study for which computational results of both classic and stochastic approaches are obtained. It is shown that, on average, with considering deterministic (stochastic) data at most 89(94) percent of the resources for Iranian power distributions units is needed to make them technically efficient.