Bridge crossings on plain rivers were modelled and scour development at the abutments and guide banks were studied. Tests were carried out in flumes 3.5 m wide and 21 m long in clear water conditions for FrR = Frf. The differential equation of equilibrium of the bed sediment movement in clear water was used, and a method for calculating the development of an abutment scour hole with time during the floods was elaborated and confirmed by experimental data (Gjunsburgs and Neilands, 2001; 2004; 2005). The local scour at bridge abutments on plain rivers starts as soon as the floodplain is flooded and stops at the peak of the flood or just after it. A new method for calculating the equilibrium depth of scour is presented. The equilibrium depth, width, and volume of the scour hole are achieved when the local velocity calculated at the flood peak becomes equal to the velocity at which starts sediment movement. The parameters of the scour hole computed during one, two, or several floods can be compared with its equilibrium parameters calculated by the equations suggested, and the risk factor of abutment scour can be determined as a ratio of hs/hequil.