Local scouring around the bridges piers has always been considered as a problem, especially in rivers. If we do not take the necessary actions to avoid the occurrence of this phenomenon or to reduce its influence, then the bridge's piers will be destroyed. Placing the bridge piers' foundation far from the earth's surface will turn out in a plan which is not economic at all. Experimental studies showed that the maximum scour depth occurring under a flood hydrograph can be much smaller than the calculated value using peak flow discharge. Thus, calculating the local scour depth around bridge piers under unsteady flow condition will be economic and will reduce the total cost. In this study, the evolution of local scour depth during the period of hydrograph has been simulated by SSIIM program. In order to verify the numerical results, the existing experimental data were used. The results show that the SSIIM program can simulate the scour depths with a good accuracy during the rising limb of hydrograph.