This paper is a summary of the empirical, scientific and methodological experience in construction of the economic and mathematical models to improve the Russian trade policy with the key partners, which are the interstate institutional associations (the European Union, BRICS, and the Commonwealth of Independent States - CIS). As a result of the study, the following conclusions were obtained: • The foreign economic cooperation with the European Union, as well as with the countries included in BRICS and CIS associations, is a multi-vector commercial space, diversified by product lines and regions for Russia; • Bearing in mind the active cooperation of Russia with the interstate associations different by the levels of economic development and institutional integration within the framework of the foreign economic cooperation, a certain update of the methodological approaches to the assessment of the efficiency and effectiveness of this cooperation is required; • A nonlinear economic-mathematical model, allowing to assess the mutual influence of the Russia's foreign economic relations with the countries included in the CIS, BRICS and the European Union, as well as to investigate the trade flows between Russia and these associations from the perspective of export and import of goods, works and services, is presented in this paper. © Serials Publications Pvt. Ltd.