Flood routing in a given reach of a prismatic channel is the process of deriving the downstream outflow hydrograph from a known inflow hydrograph at the upstream end of the channel reach. The process can be carried out by solving the basic St.-Venant (S-V) equation numerically or by using a lumped model, also called a hydrologic or black-box model, which requires calibration with observed data. The model should also be capable of reproducing the flow hydrograph at one or more intermediate points along the channel reach. This requires that at least one of the model parameters be proportional to the length of the channel reach. Another desired property of the routing model is that the outflow hydrograph produced at the downstream end of a channel reach be the same when the model is applied to the entire reach, as one unit, or when the model is applied to a number of sections or subdivisions of the channel reach in series, using the outflow of one section as inflow to the next section. The resulting outflow hydrograph at the downstream end of the reach should thus be independent of the number or lengths of the subdivisions. The above desired properties of the routing model impose certain conditions on the model or, if the model is linear, on its impulse response function (IRF). The conditions are derived in this paper and applied to two models: the linear channel model and the diffusion analogy model. ¿ American Geophysical Union 1994