Introduction. The article examines the essence of financial stability and stability of the banking system in order to analyze and understand them. The main approaches to interpreting the concept of “financial stability” were reviewed and systematized. Based on the analysis of the interpretation of the category “financial stability” by foreign and domestic scientists, two main approaches are distinguished. A forward approach aimed at determining financial stability and an inverse approach aimed at determining financial stability through the absence of financial instability. The author's definition of the concept of “financial stability” is proposed. The author's definition of the concept of “financial stability of the banking system” in accordance with the functions of the banking system is considered and formulated. The relationship between financial stability and financial sustainability, particularly in the context of the banking system, is considered and their analysis is carried out. The purpose of the article is to analyze the main approaches to defining the concepts of “financial stability” and “financial stability of the banking system”, as well as to establish the key approaches of scientists to their interpretation. Methods. In solving the tasks, general scientific and special cognitive methods were used. The theoretical and methodological basis of the research was the economic works of foreign and domestic researchers and specialists, who shed light on the issue of financial stability management and forecasting the functioning of banking systems. The following methods were used in the research process: theoretical generalization, the possibilities of which were used to generalize modern scientific theoretical approaches to defining the concepts of “financial stability” and “financial stability of the banking system”; system approach and comparative analysis – to identify connections between financial stability and financial sustainability; graphic method – for visual display of research results; method of generalization, which made it possible to formulate the results of the study. Results. An analysis of the definitions of the concept of “financial stability” by foreign and domestic scientists was carried out, which made it possible to distinguish two approaches to its interpretation. A definition of the concept of “financial stability” is proposed. A mutual and consistent connection between the financial stability of the banking system, economic development and state security was noted. The absence of a single, clear interpretation of the concept of “financial stability of the banking system” was established. An analysis of the relationship between financial stability and financial sustainability was carried out. An interpretation of the concept of “financial stability of the banking system” is proposed. Perspectives. Financial stability of the real sector of the economy cannot be achieved without the financial stability of the domestic banking system. Therefore, the important issue of developing a new scientific and methodological approach to assessing the financial stability of the banking system arises. Indicators of assessing the financial stability of the banking system are a promising direction for further scientific research.