Attempts to reduce the number of parameters in distributed rainfall-runoff models have not yet resulted in a model that is accurate for both natural and anthropogenic hillslopes. We take on the challenge by proposing a distributed model for overland flow and channel flow based on a combination of a linear response time distribution and the hillslope geomorphologic instantaneous unit hydrograph (GIUH), which can be calculated with only a digital elevation model and a map with field boundaries and channel network as input. The spatial domain is subdivided into representative elementary hillslopes (REHs) for each of which we define geometric and flow velocity parameters and compute the GIUH. The catchment GIUH is given by the sum of all REH responses. While most distributed models only perform well on natural hillslopes, the advantage of our approach is that it can also be applied to modified hillslopes with for example a rectangular drainage network and terrace cultivation. Tests show that the REH-GIUH approach performs better than classical routing functions (exponential and gamma). Simulations of four virtual hillslopes suggest that peak flow at the catchment outlet is directly related to drainage density. By combining the distributed flow routing model with a lumped-parameter infiltration model, we were also able to demonstrate that terrace cultivation delays the response time and reduces peak flow in comparison to the same hillslope, but with a natural stream network. The REH-GIUH approach is a first step in the process of coupling distributed hydrological models to erosion and water quality models at the REH (associated with agricultural management) and at the catchment scale (associated with the evaluation of the environmental impact of human activities). It furthermore provides a basis for the development of models for large catchments and urban or peri-urban catchments.