Contraction of the river flow by bridge crossing leads to streamline concentration near structures, local increase in velocity, vortex structure, increased turbulence, and development of a scour hole. Annual data on the damages of bridges because of scour evidence that not all hydraulic and river bed parameters are taken into account, and the problem is not investigated completely. The time development of scour depth at different bridge structures, such as piers, abutments, guide banks of different shape, and others, proceeds almost similarly in all cases. The scour depth is increasing rapidly at the beginning of the process and then reduces gradually. According to the test results, the scour depth depends on the uncontracted flow conditions, contraction rate of the flow, local velocity, Froude number of open flow, flow depth, grain size of bed materials, steady or unsteady flow conditions, relative depth of scour formed during the previous time, type and shape of the structure, and time. The test confirmation of the method suggested by Gjunsburgs et al. (2007) allows us to make a theoretical analysis of the dependence of relative depth of scour on the dimensionless hydraulic and river bed parameters and time, perform computer modeling of the scour process, and estimate the influence of the probability, duration, frequency, and sequence of floods on the scour depth. According to investigations performed by different authors, the angle of the flow crossing and the side-wall slope of the structure also affect the flow depth. The dependence of the relative depth of scour on these parameters was confirmed by experiments.