A necessary condition for innovative development of the economy of the Russian regions is concentrating financial resources for these goals. The basis of the innovation infrastructure in the regions are industrial clusters, with only a small part of them financially supported at the federal level. Most regional clusters lack financial resources for active innovation. Innovative entrepreneurs find funds for their projects in the form of grants and subsidies at the seed and start-up stages. However, when it comes to development of mass production, industrial enterprises lack funding. In our opinion, this problem can be solved only with active participation of regional banks through concessional financing of innovative industrial enterprises. Regional banks and innovative enterprises working closely in industrial clusters can effectively cooperate. Such banks should have a special status of regional development banks, which would provide them with a number of tax, financial and administrative benefits from the public authorities. The article presents an economic and statistical model that confirms a positive relationship between the level of development of the regional banking sector and the growth rate of the gross regional product in the subjects of the Russian Federation. Since the statistical characteristics of the model indicate an acceptable level of quality, this model can be used in forecasts of regional economic development. We have regarded this model as a confirmation of the important role of regional banks in the economic development of Russian regions. Based on the experience of foreign banking systems, we have presented the theoretical background for establishing the institution of regional development banks in Russia and offered a step-by-step algorithm for creating such banks in the regions. We have also formulated and justified the basic principles of regional development banks, presented a structural and functional model of regional clusters with the participation of financial and credit components. All the developments presented are aimed at creating conditions for the development of cluster initiatives in Russian regions and implementing all stages of the innovation cycle within the regional industrial clusters in order to ensure sustainable economic growth of the country’s subjects.