A literature review showed that finance is a driver of sustainability. However, to achieve sustainability through finance, it isnecessary to rebuild and adapt the financial system to the specifics of sustainable development. Modern financial systems can be described as one-dimensional, focusing on ensuring the economic security of transactions. Meanwhile, the growing role of risk related to non-financial factors means that the factors referred to as ESG (environmental, social, governance) become the main source threatening the stability of financial systems. Adaptation activities toward the design of so-called three-dimensional financial systems rely on incorporating ESG risk into the financial decisions of the financial institutions that make up the financial system. This is found, among other factors, in the risk assessment methodology. The general goal of the paper is to investigate which ESG criteria are incorporated into the decision-making process of financial institutions and to verify the level of sustainability of financial systems in selected OECD (Organization for Economic Cooperation and Development) countries. The main research hypothesis assumes that incorporating ESG factors into the decision-making process of financial institutions makes financial systems more sustainable. A two-stage research procedure was used to achieve the research goal. In the first stage, to determine the ESG factors that affect the level of sustainability of financial systems and identify dependencies between ESG factors incorporated by financial institutions into the decision-making process, a fuzzy cognitive map (FCM) was used. The collective map elaborating on the basis of the opinions of experts participating in the study was built using the software FCMapper_bugfix_27.1.2016. In the second stage, based on multiple-criteria decision analysis (MCDA) using the PROMETHEE method (Preference Ranking Organization Method of Enrichment Evaluation), 23 OECD countries that respect the Equator Principles were ranked according to seven groups of criteria defined for financial system assessment (financial depth, development, vulnerability, soundness, fragility, stability, and sustainability), based on a literature review. The ranking confirmed the strong position of Scandinavian countries for assuring best sustainability practices in financial institutions and in the economy. The added value of this paper can be considered at two levels: theoretical and empirical. From the theoretical point of view, it should be noted that it is the first of this kind of analysis which prioritizes ESG factors in financial decisions and ranks financial systems according to fulfilling sustainability criteria. The original empirical approach based on the two-stage research procedure provided analysis of 62 factors, of which 21 represented the environmental scope, 25 the social scope, and 16 the governance scope, which is the main advantage of the empirical study presented in the paper.