The water flow in rivers during floods has a strong impact on the transport system infrastructure – roads, bridges, dams, etc. The frequency and intensity of flood events increase with high water levels and considerable discharges, thus raising the loads on engineering structures in rivers and, at the same time, the possibility of damage. The stability of piers, abutments, guide banks, and spur dikes in floods depends on the dimensions of scour holes at foundations. By preliminary computing the scour development in time during floods, we can estimate a possible scour-depth value induced by expected floods. According to the calculated scour value, protection measures can be taken if necessary, which will reduce the economical and environmental losses. A method for predicting the damage risk of bridge structures during multiple floods is presented. The risk of flood damage is studied from the viewpoint of scouring. The method is based on two approaches to scour calculation: (1) determination of the scour development in time during multiple floods and (2) determination of the designed equilibrium depth of scour. Using these two methods, we suggest estimating the factor of flood damage risk as a ratio between the scour depth calculated during/after multiple floods and the designed equilibrium scour depth. Under critical conditions, when the scour depth calculated in floods is close to the designed equilibrium stage of scour for bridge foundations, emergency protection measures should be taken to avoid the failure of bridge structures.