Floods in cities are a worrying phenomenon as cities concentrate a growing population and activity and are expected to increase in both intensity and frequency in the context of climate change. Flood management provided by public services relies especially on 2D models that do not consider the potential street-building exchanges, considering buildings to be waterproof. A new model is proposed to represent each building as a mass conservation law and an additional source term in the classical 2D shallow water equations. A synthetic test case, with a channel and 200 buildings, shows that the buildings lead to a reduction of both the discharge (30%) and the water depth (18%) peaks in the street and generate a lag time in their time evolution. The interest of the proposed model is highlighted on the modeling of the Richelieu district (Nîmes, France): street-building exchanges impact significantly (up to 0.6 m and 1 m/s) the street hydrodynamics. The water level modifications are generalized in the synthetic case whereas they are more localized in the real-world simulation. Moreover, the model simulates the building water depth allowing for the determination of the maximal level and the submersion duration. These new results pave the way to new information for flood damage analysis and operational management.