The main objective of this research study is to simulate the scour process downstream the weirs with mathematical models for non-cohesive bed material. The basis for simulating the mobile bed is the solution of the equation for continuity of sediment by using the finite deference. Transport capacity is calculated at each cross section by using Hydraulic data obtained during the calculation of water surface profiles ( e.g. , width, depth, slope, and velocity of flow ).The results of the developed mathematical model proved that the technique is reliable in predicting the scour profile downstream weirs compared to the results of experimental data.