This thesis l concerned with the mathematical modelling of open channel flows governed by the Saint-Venant equations, which are used as a prediction or identification tools. A survey of the literature in these fields identified the problems in need of Immediate research. Numerical test runs were then devised which led to projecting a clear picture as follows. The performance of twn widely used Implicit finite difference schemes, the 4-point box and 6-point staggered schemes were compared In a wide range of circumstances. it is concluded that both schemes produce 'very close results, but the staggered scheme is prone to convergence problems In some extreme cases. It was also noted that a sharp change in geometric configuration of compound channels produced discontinuous features on the aim ulated depth and discharge hydrographs. The inability of the staggered scheme In handling a head-discharge relationship as a downstream boundary condition was tackled by proposing and implementing a scheme of second order accuracy. As model data are generally corrupted withh errors and noise, their effects together with that of other factors on the Identified friction parameters we Investigated. The results demonstte the paramount Importance of the effect of a choice of objective function on the Identified parameters. While the individual values of the identified M2nning n may vary from one flood event to another, their mean is shown both numerically and rigorously to be dependent upon the choice of objective function. It is shown that an objective function formulated by using absolute errors performs ideally and produces reliable results even in the presence of autocorrelated Gaucian noise samples. The mean of the Identified parameters is also found to be adversely affected if the observation station is affected by localized disturbances. Sensitivity of objective functions to the variation In the value of the friction parameter Is also found to be an Important factor, as Insensitivity leads to ill-conditioning.