The accuracy and efficiency of four of the more important numerical methods for flood routing are compared by simulating the propagation of the monoclinal wave in two channels with different bottom slopes. It is shown that the implicit method of Amein is in general the most suitable method for routing floods in rivers of small slope. In addition, the implicit method has maximum accuracy when the ratio of the space and time steps is approximately equal to the flood wave speed. These conclusions are not necessarily valid for flooding in estuaries.