In different spheres of human activity one needs to make decisions, connected with different risks, under condition of uncertainty. However, the very concept of uncertainty and risk needs clarification. The article discusses various interpretations of the term “uncertainty” and the formation of the term “risk” as a scientific concept. The authors prefer to limit themselves to the random-type uncertainty and propose to investigate risk and its management within the framework of this interpretation. As a tool for the problem solution construction and analysis of a risk tree is proposed. The proposed approach is demonstrated with the help of a real-world example.