This work aims to quantify the relations between the electricity demand and its main determinants in the Industrial sector of Brazil, in the period between 1974 and 2002. After identifying that the studied series were nonstationary, the use of the Cointegration Approach and an Error-Correction Mechanism was opted . The results obtained have turned out as according to the expected. The industrial electricity demand is price inelastic in both short and long run. The results still pointed out that such demand is inelastic to income in the short run, but elastic in the long run. The parameter estimated for a substitute factor to the energy was not significant, indicating that there is no close substitute for electricity in the Industrial sector. This fact evidenced the necessity of a program of reorganization and expansion for the Brazilian Electrical system as condition for the maintenance and the growth of the industrial activity in the country.