An explicit finite difference scheme for erosion and sediment transport on upland areas of a watershed is derived. The derivation is based on the unsteady state one-dimensional sediment continuity and momentum equations, simplified with the kinematic wave approximation. The derivation ends up with a linear partial differential equation. Upland erosion is thought of as sheet erosion incorporating the effects of rainfall and runoff by way of nonphysical calibration parameters. Calibration of these parameters is of great importance for ungauged basins where data do not exist. A finite difference scheme is chosen to solve the resulting equation, together with appropriate boundary and initial conditions. A hypothetical data set was used to evaluate the applicability of the model developed in the study. The performance of the model at the hillslope scale indicates that it has potential for application at the watershed-scale.