A rainstorm that caused a severe flash flood on the piedmont plain at the toe positions of two alluvial fans located to the west of the Organ Mountains in Dona Ana County, New Mexico, USA, is analysed. The space–time distributions of rainfall are evaluated from the Next Generation Weather Radar (NEXRAD) and overland flow is modelled as kinematic wave. The spatial distribution of rainfall shows a topographic control. The greatest rainfall depth, duration, and intensity occurred at the higher elevation mountain slopes and decreased with decreasing elevation from the alluvial fans to the piedmont plain. The alluvial fan–piedmont plain system is modelled by coupling divergent and rectangular overland flow planes. Explicit finite difference approximations, hybridized with the analytical method of characteristics, are made to the kinematic wave equations to account for the spatial and temporal distribution of the rainfall and variable boundary conditions. Simulation results indicate that sheet-flow floodwater elevations rise (1) in a nonlinear fashion from the apex to toe positions of the alluvial fans, and (2) near linearly from the toe positions of the alluvial fans onto the piedmont plains with the formation of kinematic shocks near the middle to the upstream end of the plane at times between the initiation of the rainstorm and the time of concentration of the plane. Thus, the maximum flooding occurs at the middle or upstream sections of the piedmont plains regardless of the pattern of space–time variability of rainfall. These results are in agreement with observed geomorphologic features suggesting that piedmont plains are naturally flood-prone areas. This case study demonstrates that flood hazards on piedmont plains can exceed those on alluvial fans. The models presented in this study suggest that the flood hazard zones on coupled alluvial fan–piedmont plain landforms should be delineated transverse to the flow directions, as opposed to the flood hazard zones with boundaries in the longitudinal direction of the axis of an alluvial fan. Copyright © 2003 John Wiley & Sons, Ltd.