The objective of this study was to obtain an estimate for residential electricity demand in Minas Gerais in the period from 1970 to 2002. Specifically, the goal was to estimate price and income elasticities. After determining that the series under study were non-stationary, we chose to use the Co-integration approach, estimating a Vector Error Correction Model (VEC Model). The results obtained show that the demand studied is more sensible to variations in the income than to the price of the electricity, although both elasticities are inferior to the unit. It was also concluded that price-elasticity is higher in Minas Gerais than it is for Brazil as a whole, suggesting differentiated usage of this energy among the different states in the Country.