mathematical model is developed for furrow surface irrigation design using BASIC language to simulate all stages of the hydraulic movement of water and evaluate the performance of the accounts design of surface irrigation lines as well as to assess alternative designs for field and administrative operations. The developed model is based on the volume balance method considering the target application depth which solved by the Newton-Raphson procedure. Model performance is evaluated and verified using field data. Field experiments were conducted during 2013-2014 at a sugar crops research station- Alexandria; in clay soils. Measurement parameters included soil roughness coefficient; furrow shape parameters; (slope; width; and length) advance and recession times; cutoff time and furrow water normal depth through irrigation event are utilized to verify the accuracy of the developed model. Three different inflow rates 1.22; 1.48 and 2.37 (l/s) and different furrow construction shapes (Triangular; Rectangular; Trapezoid and Parabola) are used. The developed mathematical model is capable to select which furrow shape should use; and determine and predict water infiltrated depth parameters equations (a and K) for any inflow rate can used. Knowledge of each of furrow cross-sectional area; the advance time to half furrow length; and advance time to the overall furrow length; volumes of water applied for each of half furrow length and overall furrow length should be predicated. By comparing the obtainedmodel predicted date with field date; the results showe that the developed model accurately predict the hydraulic design of furrow surface irrigation and water infiltrated depth parameters as it is applicable in practice in design and contribute to the advisory work for water conservation and economic use of water.