An analysis of the existing work on the theoretical description of the passage of a dam-break wave shows that there is a certain foundation in this area of research, contributed by both foreign and domestic researchers, as well as by the authors of the present study. There is a need to improve the calculation methodology and to carry out additional theoretical and experimental studies to address this issue. The study examines the problem of water overflow over a dam crest, which allows for the determination of the flow thickness and velocity downstream of the dam in order to ultimately assess the parameters of the formation of the dam-break wave and the scale of destruction downstream of the structure. A hydrodynamic model is proposed for the analysis, representing the flow of a viscous fluid over a polygonal weir. Based on existing research results available in the literature, a description is provided of the problem of water overflow over a dam crest, which allows for determining the flow thickness and velocity downstream of the dam in order to ultimately assess the parameters of the dam-break wave formation and the extent of destruction downstream of the structure. It was carried out the modeling of occurrence of emergency situation on high-mountainous lakes of the Tashkent oblast in case of full or partial destruction of natural dams.