Globalization of modern economics forms new economic challenges in order to improve Russian regions’ competitiveness. The regions’ competitiveness significance grows substantially under conditions of the regions’ historically formed economies’ focus; current nature resources use potential and the advantages of the regions’ geographic location for external economic cooperation. Considering these facts, current research suggests a new method of assessing the socio-economic systems’ competitiveness. The authors suggest using the socio-economic system’s competitiveness integral index as the basic competitiveness assessment means. This integral index comprises 4 indicators, defining the system’s functionality, system, proactiveness, and organicity. It is suggested to form private competitiveness indices in long-term and short-term periods in order to assess the system’s competitiveness dynamically. The private competitiveness index in short-term period comprises indicators, defining the functionality and system levels, and the private competitiveness index in long-term period comprises defining the proactiveness and organicity levels. Several economic magnitudes, interpreting the functionality, system, proactiveness, and organicity indicators are presumed for interpreting each of them. A broadened spectrum of economic magnitudes, used for interpreting the assessment indicators, facilitates the involvement of various statistic and empiric data.