||Predicting the unsteady flow behaviour in open channel systems is a complex computational problem. It is generally recognized that the Method of Character-istics (MOC) best represents the physical nature of transient flow phenomena, but difficulties associated with discretization and interpolation in a fixed grid have made this scheme less populu than other explicit/implicit finite alternative approach to interpolation involves adjusting the tic lines and integrating along the adjusted characteristics. difference methods, An slope of the characteris. This recently developed Modified Characteristics Scheme now makes MOC less attenuative and, thus more computationally competitive with other finite difference techniques. The modified characteristics approach uses a new transformation of the original partial differential dynamic and continuity equations governing unsteady flow into characteristic form based on the total derivative concept. In applying the technique to transient flows, the analyst is allowed to distort the physical problem by artificially accelerating the wave signal and then corrects the wave by an approximate integration of additional partial differential terms that arise from the transformation procedure. In this thesis, a family of numerical schemes based on this new MOC approach, referred to as the Modified Method of Characteristics schemes (MMOC), are derived for the purposes of investigating an alternative method for computing unsteady open channel flow. It is found that, in the simplest of formulations, the MMOC scheme performs better than the space line interpolation scheme, and has the advantages of simplicity and efficiency. With marginal adjustments, the numerical performance of the MMOC scheme exceeds that of its traditional counterpart. Convergence properties of each formulation within the MMOC schemes are established numerically and, wherever possible, theoretically. Comparisons in performance are drawn with an analytic problem, a benchmark converged solution and with the traditional space line interpolation technique. A new approximation technique within the MMOC formulations is developed and is shown to be capable of dealing with non-linear instabilities that arise from the traditional representation of the friction term, without explicitly treating the friction equation, or by manually reducing the Courant number. The K-linearized MMOC scheme is shown to be superior to space line interpolation, in that a wider range of Manning's friction coefficients can be modeled with a given discretization and improved numerical stability. Also, in this work the energy equation for rectangular channel systems is used as a means for assessing the performance of each MMOC formulation.