According to the Federal law № 117-FZ "On the safety of hydraulic structures", an owner of a hydraulic structure has to develop a declaration of safety of the dam. It should include the potential accident scenarios with assessment of the probabilities of their realization. The methodology of the development of scenarios and the water overflow probability that is one of the basic causes of the emergency situations at the dams is given in the study. The causes of the spillway failure and most frequent events leading to the failures or disturbances of the spillway structures are analyzed. The probability assessment of the water overflow across the dam crest using the fault tree method is given. Within the framework of this method various heuristic procedures may be most adequately realized and for the probabilistic assessment of the basic events the methods of the statistical and / or expert’s reliability assessment may be used besides the parametric reliability theory methods. Such an approach permits to unify the procedure of the probabilistic assessment of the water overflow across the dam crest. The general form of the event tree “Overflow across the crest” or in other words fault tree that leads to the water overflow across the dam crest is presented. The application of this approach is illustrated by an example of estimating the probability of the scenario of an emergency related to the overflow the reservoir on the Lower Bureya HPP in case of emergency release from the reservoir of the Bureya HPP. The analysis of the fault tree makes it possible to form a logical model of the origination and the development of the complex processes and phenomena leading to the water overflow across the dam crest and permits to make the quantitative and the qualitative analysis of the event with the assessment of the overflow probability.