A one-dimensional uncoupled model governed by this research is a physics-based modelling of the rainfall-runoff induced erosion process. The presented model is composed of three parts of a three-dimensional (3D) hillslope geometry, a nonlinear storage (kinematic wave) model for hillslope hydrological response, and an unsteady physically based surface erosion model. The 3D hillslope geometry model allows describing of the hillslope morphology by defining their plan shape and profile curvature. By changing these two topographic parameters, nine basic hillslope types are derived. The modelling of hillslope hydrological response is based on a flow continuity equation as the relation of discharge and flow depth is passed on kinematic wave approximation. The erosion model is based on a mass conservation equation for unsteady flow. The model assumes that suspended sediment does not affect flow dynamics. The model also accounts for the effect of flow depth plus loose soil depth on soil detachment. The presented model was run for two different precipitations, slope content, and length, and results were plotted for sediment detachment/deposition rate. Based on the obtained results, in hillslopes with convex and straight profile curvatures, sediment detachment only occurred in the whole length of the hillslope. However, in concave ones, sediment detachment and deposition only occurred together in hillslope. The hillslopes with straight profiles and convergent plans have the highest rate of detachment. Also, results show that most detachment rates occur in convex profile curvatures, which are about 15 times more than in straight profiles. Copyright © 2015 John Wiley & Sons, Ltd.