This paper investigates some aspects of the interrelated paths of economic growth and energy demand, in the case of an industrializing economy, through the use of numerous econometric models. Translog functions have helped establish that income and price elasticities of energy, two critical parameters in the energy-economy interaction, exhibit falling trends with time. The value share of the industrial sector is strongly associated with both energy demand and energy intensity. Any increase in the former will lead to amplified increases in the latter, rendering the continuation of past trends in industrial expansion questionable under conditions of high energy costs. Substitution among capital, labor and energy does take place, though to a limited extent, as indicated by the aggregate measure of energy/non-energy substitution elasticity. All findings appear to suggest that energy policymaking, in an industrializing country like Greece, will be of low effectiveness until certain structural changes in the economy are realized.