This study is aimed at identifying the best values for the parameters of energy efficient digital development of the petroleum and gas sector. Research methods - construction of a production function, regression analysis and linear programming. Based on the production function of Cobb-Douglas, the dependence of the sales volumes of the petroleum and gas sector of the economy on the costs of digitalization and labor costs was revealed; the regression analysis method provided the construction of a set of equations describing the impact of the costs of energy resources of petroleum and gas enterprises and the costs of digitalization on the total costs of enterprises for production and sales, the efficiency of using by-products from petroleum production and labor capital; the optimal values of energy-efficient digital resource-saving development of the petroleum and gas sector of the economy have been determined, the achievement of which will ensure a decrease in the energy consumption of processes at the enterprises of the petroleum and gas complex. Thus, connections have been established and the trajectories of energy efficient functioning of the petroleum and gas sector of the economy have been determined. The research results can be applied within the framework of strategies for socio-economic development, sustainable development, as well as digitalization of the petroleum and gas complex and industrial enterprises.