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