The objective of this study was to work out a method for prediction of the safety and stability of hydraulic structures in river floodplains during multiple floods because of scour. A differential equation of equilibrium of the bed sediment movement for clear water was used and a method for computing the scour development in time at abutments in river floodplain during multiple floods was elaborated. A method for computing the equilibrium stage of local scour at abutments in the river floodplain was also developed. Methods were verified by experimental data. Influence on the equilibrium time of such factors as flow contraction rate, relative flow velocity, Froude number, relative grain size of bed materials, stratified bed conditions, and the time interval duration was also studied. For flood damage assessment the proposed scour calculation methods are used.