The flow parameters at the peak of the flood with unrestricted or restricted duration and the approach flow velocity are used in most accepted methods for local scour calculation, but in nature the flood has a form of hydrograph and unsteady flow conditions must be evaluated. At the present time, there is no formula or method for finding the scour depth near water engineering structures in the flow reflecting the changes of hydraulic and river bed parameters during multiple floods. A new method to calculate the development of the depth, width and volume of the scour hole in time during multiple floods has been developed. Based on the agreement of experimental and calculated results, the computer program was carried out to model time-dependent scour development during a single flood with different slope of hydrograph and during multiple floods with different duration, probability, frequency and sequence. The analysis of the influence of multiple floods with different probability, duration, sequence and frequency showed that, with less probability, increased duration and frequency of the floods, and certain sequences of different probability, the scour depth, width and volume increases. It was confirmed that the scour development for a single flood depends on the continuous changes of the hydraulic and river bed parameters because of the changes in flood discharge and the depth of the local scour hole near the water engineering structure. The scour which developed after the previous flood must be taken into account when the influence of the forthcoming flood on scour depth is evaluated. The influence of the steepness of hydrograph limbs was also studied and analysed. Significant changes in maximum scour depth developed during single wave floods with a different hydrograph steepness were not found, however a direct impact to the time when maximum scour is developed was found. It was confirmed that during the local scour evolution the local velocity increases and the critical one decreases because of increased discharge and the scour hole developed. The scour stops when the local and critical velocities become equal. The figures are presented which confirm the difference of local velocity from approach velocity near the water engineering structure. It was confirmed that the local velocity, but not the approach flow velocity as accepted by different authors, forms the scour hole.