The environmental impact of subsurface drainage and agricultural activities has been widely studied in the literature. Agricultural subsurface drainage modifies the hydrological behavior and accelerates the transfer of pollutants of agricultural origin into surface water during the drain flow period, which is often limited to winter. The main objective of this study is to present a modeling approach allowing an accurate modeling of subsurface drainage discharge and prediction of drain flow start times, by integrating a new conceptual soil reservoir, managing the water flow in the unsaturated zone, to the SIDRA model. A comparison of the model results with field measurements of drainage discharge at the "La Jaillie`re " site (France) shows that such a model can efficiently simulate drainage discharge (KGE values > 0.75) and predict, with good accuracy, the drain flow start time (with a median value of 5 days and a standard deviation of 10 days). The split simple test conducted for the model calibration and validation shows that the model is temporally robust. A sensitivity analysis conducted using the Sobol method on the five model parameters reveals that the drainage discharge simulation is mainly sensitive to the hydraulic conductivity and drainable porosity parameters. On the other hand, the date delimiting drain flow start is sensitive to the soil reservoir parameters. The model's ability to accurately predict the start of drain flow serves to avoid the application of farm inputs (pesticides or fertilizers) during this critical period in order to limit their transfer to surface waters.