Existing approaches to the analysis of countries economic integration processes in international practice are investigated in the paper. Evaluating methodology of the long-term integration processes in the electric power sector is offered for the EAEU countries in three scenarios: High, low and medium, based on the synergy of various economic and mathematical methods. The actual methodology is formed in accordance with special macroeconomic scenario conditions and includes the final energy consumption forecast with division by the types of energy sources in the context of consumers categories of the EAEU countries based on generated scenario conditions using econometric methods (growth curves, Cobb-Douglas production function, regression analysis, simulation methods), as well as the development forecast of electric power industry concerning the EAEU countries reasoning from perspective dynamics of generating capacities of these countries. Project growth of electric power sector development founded on suggested method was made for the EAEU countries for the period of 2018-2040, specifically, electricity consumption projection, electricity consumption increasing, as well as capacity increasing of NPGS, HEP and RER in these countries. The necessity of further efforts to develop the common electric power market in the EAEU countries in order to obtain possible long-term integration effects are emphasized.