This research project aimed to enhance numerical methods for handling transcritical flow in river systems, particularly at branches and varying cross-sections. The goal was to develop a numerical computer model capable of accurately simulating and analyzing river flow under transcritical conditions. The project results include development of an improved numerical model capable of handling transcritical flow in river systems. The research findings and model advancements contributed to the understanding and management of flow behavior in steep rivers, leading to more accurate and effective flood forecasting, river engineering, and water resources management practices.