Analysis of the literature shows that there are no methods or formulas to calculate the equilibrium time of scour near elliptical guide banks. In the formulas used in calculating the equilibrium time of scour at piers or abutments, different parameters are not taken into consideration. The differential equation of the bed sediment movement in clear-water was used and the method for computing the equilibrium time of scour near elliptical guide banks was elaborated. New hydraulic threshold criterion is proposed for the calculation of equilibrium time of scour. Analysis of the proposed method shows the influence of the following parameters on the equilibrium time of scour: contraction rate of the flow, Froude number, bed layering, sediment movement parameters, local flow modification, relative local and critical velocities ratio, and relative depth. Computer modeling results were compared with the equilibrium times of scour which were calculated by the presented method and they were in good agreement.