The development of this model will allow to possess a computational tool to design adequately the system of border irrigation, reducing the water loss and using in an ideal way to improve the productivity of the cultures, under the premises of efficient use of water, that is to say cultures of major productivity, to the lowest consumption of water, using methodologies of production optimal. Was implemented the numerical scheme in finite volumes for the equations of flow Saint Venant, which allowed knowing the profile of superficial flow and the infiltration in the soil according to the advance of the irrigation. After the process of simulation of several, cases, was managed to establish that the longitudinal slope plays an important paper in the flow for the border irrigation according to the raised model the slope must be minor 0,001 m/m. The major slopes generate rapid or supercritical...