The damage of engineering structures in rivers, because of scour (near intakes, pumping stations, bridge structures – abutments, guide banks, dams, etc.) leads to considerable environmental and economical losses. During multiple floods the scour hole parameters, under clear-water conditions, are summed up, increases in time and can be reason of foudations failure. The differential equation of equilibrium of the bed sediment movement in clear water was used, and a method for calculating the scour development with time at the engineering structures under stratified bed conditions(intakes abutments, guide banks) during the multiple floods was elaborated and confirmed with experimental data .