For the world economy, the integration process is one of the most widespread and global. The Eurasian Economic Union is a typical example of bringing countries together to achieve shared goals and to face diverse challenges successfully by implementing coordinated policies and harmonizing the regulatory framework. The formation of a monetary union will be the next stage of integration. The EAEU member States need to achieve a certain level of economic convergence for that purpose. Thus, the main aim of this research article is to analyze some of the economic indicators of the EAEU in order to identify common problems, the solution of which will be necessary for the successful formation and functioning of the monetary union. The authors have studied such indicators as GDP volumes and inflation levels, as well as the dynamics of changes in exchange rates and the level of mutual direct investment in terms of sigma convergence. The authors have also used methods of graphical representation of the scientific results. The reports of the Eurasian Economic Commission and the Central Banks of the EAEU Member States were used as the main sources of statistical data.