Flood risk is the natural phenomenon that affects the most people in the world, and climate change is likely to increase this trend. Floods, whether in rivers or in urban areas, carry debris that can have a significant impact on hydrodynamics and therefore on risk. Although numerical models are frequently used to anticipate the impacts of floods in order to improve land-use planning and facilitate crisis management, there are few models capable of representing accurately both the flood hydrodynamics and the associated debris transport process. Numerical models, when they exist, are generally based on simplifying assumptions. In this paper, we propose a new operational model that is validated and compared with analytical results, other models and experimental data. The proposed model, implemented in the SW2D software, paves the way for a better representation of debris clogging on hydrodynamics, even with a large number of transported objects.