The essential purpose assigned to this present research is the contribution to the development of a model numeric two-dimensional permitting the simulation of a transient flow to free surface, quickly varied, resulting of a total and instantaneous rupture of a dam in a rectangular channel. For that to make, we present in a first section, the representative mathematical model of this flow, based on Saint Venat equations two-dimensional. An algorithm in finite differences is developed then to resolve this system of equations. The algorithm for needs of our research is to fractional step, based on the numeric diagram of Mac Cormack. During this simulation, we put in evidence the evolution in the time, the height and the speed of the flow in different positions, and this until drains it of the dam. We are also interested to the survey of the certain parameter influence on the flow as the slope of the bottom, the roughness of Manning and the initial height of water in the reservoir. Finally to validate and to test performances of the model developed, we did several applications in the second section, then compared results gotten to the experimental and numeric results.
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