A theoretical model is presented to estimate the time-variation of scour depth in an evolving scour hole at circular piers under clear-water and live-bed scour conditions with uniform and non-uniform sediments. The procedure developed for computing the time-variation of scour depth was based on the concept of the conservation of the mass of sediment, considering the horseshoe vortex system to be the main agent of scouring and assuming a layer-by-layer scouring process. The present model corresponds closely with the experimental data of time-variation of scour depth under clear-water and live-bed scour conditions with uniform and non-uniform sediments reported by various investigators. Computation is extended up to the equilibrium scour condition and the corresponding design formula for estimation of maximum scour depth is also proposed for given flow, sediment and pier conditions. The computed values of maximum scour depth showed adequate and safe estimation for bridge pier foundations. A theoretical model is presented to estimate the time-variation of scour depth in an evolving scour hole at circular piers under clear-water and live-bed scour conditions with uniform and non-uniform sediments. The procedure developed for computing the time-variation of scour depth was based on the concept of the conservation of the mass of sediment, considering the horseshoe vortex system to be the main agent of scouring and assuming a layer-by-layer scouring process. The present model corresponds closely with the experimental data of time-variation of scour depth under clear-water and live-bed scour conditions with uniform and non-uniform sediments reported by various investigators. Computation is extended up to the equilibrium scour condition and the corresponding design formula for estimation of maximum scour depth is also proposed for given flow, sediment and pier conditions. The computed values of maximum scour depth showed adequate and safe estimation for bridge pier foundations.