Surface irrigation projects which accounts for almost all of the irrigated land areas of the world has been studied extensively by many investigators and their performance was found to be lower than expected. Many of these projects are built and operated without adequate technical input, with consequent low uniformity and efficiency of water application. However, irrigators are still faced with significant challenges in making both design and operation of surface irrigation systems more efficient. In this study a mathematical design approach for furrow irrigation was developed as spreadsheet model to simulate all hydraulic phases of water movement as aid to design and to evaluate the performance of furrow irrigation. The irrigation model simulates the hydraulics of furrow irrigation at the field scale. The principle role of the model is the evaluation of alternative field layouts (field length and slope) and management practices (water application rates and cut-off times). Input data requirements for the simulation component include field length, slope, infiltration characteristics (or advance data), target application depth, water application rate, Manning's resistance and furrow geometry. A series of simple relations were presented for estimating the advance, recession, and performance of surface irrigation systems. The approach uses continuity to compute the advance time to field end and half the distance to field end. The irrigation methods differ slightly in how the surface volume is computed. Initially a surface shape factor is used to compute storage volume during advance phase; however, estimation of this storage volume was corrected during storage, depletion and recession phases by utilizing Muskingum-Cunge routing method. The subsurface volume calculations use a modified Kostiakov equation that includes both an initial sink term and a constant final infiltration rate. Recession calculations differ for each method. With sloping methods, adjustments to a straight line recession curve make recession estimates more reasonable. It is shown that the procedure can produce reasonable predictions of design performance over a range of conditions. Model verification was made by its comparison with FAO-surface-model, and zero-inertia model using data from furrow fields of Kenana Sugar Scheme-Sudan.