The paper focuses on the study of the problems of the economic and mathematical modeling of the green economy at the regional level. The purpose of the research is the development of economic and mathematical tools for the economic and ecological systems’ modeling at the regional level on the basis of the principles of green economy. The hypothesis of the research is based on the thesis that in the conditions of the exhaustion of natural resources and depletion of natural capital, the technogenic fields, production and consumption waste could be considered as a resource basis for modernization. Such factors’ use leads to the elimination of accumulated environmental damage and substitution of natural resources. The paper describes the approaches to the system modeling problem-solving in order to develop the green economy both in the country and its regions. The urgency of the transition to a green economy is confirmed by the theoretical and practical research on the cyclical development of the socio-eco-economic systems. A number of formalized models and methods for solving the current environmental and economic issues including the economic valuation of accumulated environmental damage, eco-economic assessment of the efficiency of natural resource substitution with resource-substitute are proposed as well as the choice of an optimal set of resources-substitutes taking into account the financial and natural resource constraints. The authors research the typical model of green growth considering the exhaustion of natural resources, technogenic resources deposits involving in economic circulation through the implementation of investment projects on the elimination of accumulated environmental damage. The results could be used in the different regions of Russia for the justification and implementation of investment projects within the framework of the federal target program “Elimination of accumulated environmental damage” in 2015–2026 years.