In the assessment of financial risks of enterprises in the non-financial sphere, and in small and medium-sized enterprises in particular, it is recommended that the principles of Occam and KISS (keep it simple, stupid) be used as guidelines. The application of these principles in relation to the choice of the methods of financial risks assessment means that mainly simple methods - and those known by enterprise specialists - should be used. These sufficiently simple methods are the following: special ratios method and expert examination method. The author evaluates the development of discriminant and conditional probability methods of financial risk assessment in nine East European countries. The usage of these methods enables small and medium-sized enterprises to assess, predict and manage risks related to liquidity, credit, decreasing financial stability and insolvency/bankruptcy. In doing this research we applied an approach built on conditional probability models (logit and probit analysis) on source reviews and the author's own experience. Selection and assessment of the described models of insolvency/bankruptcy and provisions of financial risk assessment are based on the author's personal opinion. The chapter proceeds as follows: after the introduction in Section 2 the financial risk definition is introduced and a three-level classification of financial risk is presented. Next, in Section 3 the development of financial ratios will be described and a review of using classic models for assessing insolvency/bankruptcy, multiple discriminate analysis (MDA) type models and their development in nine countries of Europe are given. Then in Section 4 a discussion will be conducted about the usage of express analysis of financial risks on the basis of the principles of the analysis of enterprise economic turnover balance sheet and quick tests as a simple instrument. Tests to assess the risks to the enterprises at different stages of the life cycle will also be discussed. At the end of chapter 4 a case study of the risk occurrence reasons is provided. It is possible to position these factors on a scale of risk probabilities by employing expert assessment. In Section 5 a critical evaluation of the methods of measuring the financial risks of enterprises in the non-financial sphere are discussed and future ideas are given. At the end of the chapter we offer some concluding ideas. In the appendix, we attach reference materials containing 31 models, developed in nine countries enabling determination of enterprises’ and their partners’ insolvency risk.