The linear flood routing model presented has been derived from the linearized St. Venant equation for the case of a uniform open channel with arbitrary cross-sectional shape and friction law. In order to filter out the downstream boundary condition the kinematic wave solution is used to approximate the diffusion term in the St. Venant equation. The hydrodynamic model obtained is called the rapid flow model (RFM). It provides the exact solution for a Froude number equal to one. Such characteristics of the RFM impulse response as cumulants, amplitude and phase spectra are analysed, and then compared with those of the complete linearized St. Venant equations for different reach lengths, values of Froude number and frequencies of flood waves. The RFM can be applied for mountainous rivers that have large Froude numbers and both quick and slow rising waves.