A partial covering mulch of residue on the soil strongly affects runoff dynamics, which consequently substantially reduces runoff amount. Experiments were conducted in la Tinaja (Mexico) on runoff plots (RPs) (20 m2) of four different treatments (bare, unplanted with 1.5 t ha-1 of residue, planted with 1.5 and 4.5 t ha-1 of residue), to characterize mulch effects. During one crop cycle, rainfall and runoff flow were recorded at a 20 s time step. Soil moisture, crop leaf area index, saturated hydraulic conductivity and sorptivity were also measured. Mulch increased the infiltration rate of the topsoil layer, concentrated overland flow and slowed it down by increasing roughness and pathway tortuosity. The physically based model developed accounts for these mulch effects on runoff. The model consists of a production and a transfer module. Each RP is considered as a microcatchment drained by a single channel. The production module accounts for rain interception by the plant and the mulch, soil retention and infiltration. The excess rainfall that cannot infiltrate defines runoff and is concentrated in the channel. The transfer module governs runoff flow out of the RP according to Darcy-Weisbach's law. The model was calibrated on 12 events (five parameters). Fitted parameters provided high Nash efficiencies ranging from 0.721 to 0.828. Both runoff hydrographs and volumes were well simulated. A sensitivity analysis was carried out on eight parameters and a partial validation was done on 14 independent events. The model can be used as a predictive tool to assess the effect of various types of mulch on runoff. All its parameters are physical and can be measured or derived from literature. The model can also simulate inner variables of interest (water depth in the channel, infiltration in the channel and the hillslopes, etc.) at any time during rainfall.