This paper is concerned with a mathematical model for simulating hydrodynamics of 1 D flood f lows with the WEN O ( Weighted Essentially Non - oscillatory Scheme ) scheme. The time di scretization uses the Runge - Kutta TVD ( Total Variation Diminishing ) scheme. By using the model, the flow property of d am - b reak was calculated, and the flow velocity and water depth were obtained. The calculated results show that the WENO scheme has higher a ccuracy and better stability, and has the ability to automatically capture shock waves, and may suppress the oscillations of numerical solution. This model can effectively simulate the hydrodynamics of 1 D river flow .