Characteristic diagrams of the distribution of longitudinal velocities in the local scour zone at partly submerged obstructions are shown, and an equation is presented of dynamic balance of the flow around an obstruction during the the period of stabilization. Equations are also presented relate the nonscouring velocity in the hole at the time of time of stabilization of the local scour. The velocity of redistribution in the local scour hole and its dependence on the Reynolds numbers is discussed. The hydraulic modelling of the process of local scour is described, and the effect of slow time variability of the flow parameters during passage of a flood on the local scour is considered, as well as the process of channel deformation at a separately standing pier. The results are discussed of studies of scour at circular, square, and rectangular piers. The studies showed that the most poorly steamlined section was the square, and the best was the circular section. The maximum scour depths were recorded for the square-section barrier and the minimum for the circular-section barrier.