This investigation presents a spectral method for solving the one-dimensional shallow-water wave equations. The spectral method is based on the Chebyshev collocation technique and finite-difference time stepping. The spectral method and finite-difference Preissmann scheme are applied to route a log-Pearson Type III hydrograph through a wide rectangular channel, and the results are compared. The spectral method performs better than the Preissmann scheme as long as the time-stepping errors are kept low. However, for larger time steps, the Preissmann scheme, which is almost second-order accurate in time (and second-order accurate in space) performs better than the spectral scheme, which is first-order accurate in time and has so-called infinite-order accuracy in space. This seems to indicate that the order of accuracy in time discretization is more important than that in space discretization, in numerical models, for fast-rising floods and friction-dominated flows. © ASCE.