The article is devoted to research methods of diminishing risks for technogenic accidents, natural and ecological disasters, catastrophes and emergency situations. In this paper substantial attention has been paid to ecological aspects of technogenic accidents. During research a better introduction to the concept of “acceptable risk” has been made. Accident development scenarios are becoming increasingly sophisticated. Procedural framework for assessing operation of dangerous objects is still at the development stage, and, as the analysis shows, quite frequently the task is solved with the help of various methods in order to develop reliable scenarios and estimate the accident consequences.