River flow contraction by engineering structures (intakes, embankment, abutments, spurs, guide banks) to flow leads to flow pattern modification, concentration of streamliners, sharp drop in water level, local increase in velocity, and development of scour hole. Damages or failure of engineering structures in flow because scour at the foundations under stratified bed conditions is an important problem, which is not studied well. The differential equation of equilibrium for the bed sediment movement for clear-water conditions is used and a method for computing the scour development with time at the elliptical guide banks is elaborated. The method is confirmed by experimental data. This method allows one to calculate the scour depth development under stratified bed conditions with different thickness and sequence of the layers. The most critical conditions for structures occur when a fine-sand layer is under a coarse-sand layer. According to the results obtained in tests and by the method presented, the depth of scour is always greater when a fine-sand layer is under a coarse-sand layer(s). Using the mean grain size on the top of the river bed for calculation the depth of scour, neglecting stratification, can lead to the wrong results and possible damages and losses.