A discrete random particle representation of flow processes on shallow hillslopes is compared with solutions of the classical kinematic wave representation. The discrete Multiple Interacting Pathways (MIPs) model has the potential to represent the effects of complex heterogeneities and preferential flow pathways. It is shown that, under shared assumptions, the MIPs model can produce equivalent flow predictions to a standard kinematic wave realisation. The MIPs model is then used to further explore the relationship between celerity and water velocity by introducing a velocity distribution, which represents the range of possible flow pathways, and therefore is representative of the nature of heterogeneity (or lack of it within a homogeneous case) within the subsurface. It is shown that whilst flux constraints can be satisfied with a distribution of flow velocities, it can result in changes to the hydrograph. Multiple pathways also have an influence on the residence times for input increments, output increments and storage in the system.