Flood hazard studies for dam break cases are of utmost importance for understanding potential risks and minimizing the impact of such accidents. Siriu Dam, which has a clay core, is ranked as the third highest embankment dam in Romania. A fully dynamic 2D hydraulic numerical model was developed using HEC-RAS software to simulate the routing of the flood waves formed by breaching this dam. Four different failure scenarios were considered: two for overtopping and two for piping. The breach parameters were chosen based on the dam characteristics in accordance with appropriate empirical relationships. The flood hazard was quantified and analyzed in terms of depths, velocities, depth x velocity values, and flooded areas. The results provide useful information concerning flood risk mitigation, such as the dam break wave routing, peak discharges, arrival time, travel velocity, and inundation boundary. The influence of the scenario and site characteristics (topography, river morphology, and constructions) on the results was analyzed. Depths and velocities over 10 m and 15 m/s, respectively, were obtained close to the dam, while those in Buzău City (90 km away) were under 1 m and 2 m/s, respectively. The city was flooded 7–8.5 h after the breach (depending on the scenario), and over 15 to 50% of its total area was affected. Moreover, the flood hazard parameters were compared for the different scenarios, providing the practical details necessary to develop flood risk management plans and the associated response measures for the inhabited areas. This is the first numerical study to simulate the impact of a potential break accident that can occur for this dam.