Abstract-Under current conditions it is impossible to manage a company to a good quality without specialized instruments. Currently decision support systems (DSS) are widely used to manage the bankruptcy risks of a company. Developing a DSS requires proper mathematical models. It allows return on capital forecasting and financial solvency revealing and, mainly, regulating the risk of bankruptcy event.The aim of the given paper is to throw light on the problem of decision support system development when estimating financial stability of companies. In the paper we consider the mathematical support of DSS -models of financial stability estimation and dynamic model of managing the resultant index of financial stability. In the paper we review the methods of bankruptcy risk estimation described in academic literature and describe some models developed by the authors.In the paper the authors provide a brief review of DSS designed for managing the bankruptcy risk of companies, analyze the financial stability of 30 oil and gas companies organized as open joint stock companies. It was shown that there are no universal models for estimating company bankruptcy risk. The limits to applicability of the models depend upon the economic conditions under which the models were developed, notably, it was shown that foreign models are insufficient for Russian conditions. The authors provide their models of financial stability estimation of oil and gas and machine-building companies which allow taking into consideration quantitative and qualitative indices which can be both standardized and non-standardized. The models allow taking into account industry-specific peculiarities of companies and can be applied to estimate the bankruptcy risk. (Abstract) Keywords -systems of decision support, financial stability, bankruptcy, bankruptcy risk models, factor analysis, discriminate models, fuzzy set models