Several numerical and hydraulic aspects of river modelling are studied in two parts. Part I deals with the investigation of the flow characteristics in the lateral and vertical directions. The concepts and assumptions adopted in a theoretical model for the description of turbulent flow are addressed. Certain experimentally derived coefficients required by the model are investigated using the data from the UK SERC-FCF. It is followed by the implementation of a finite element computer model called RFMFEM to obtain a solution to the depth averaged momentum equation. The model can describe the lateral distributions of depth mean velocity and Reynolds shear stress, and the local boundary shear stress in channels of any cross sectional shape. Benchmarking and validation of the model is attained by comparisons with an analytical solution and experimental data. Through the lateral integration of the flow to give the discharge, the model may also predict the stage-discharge relationship. Likewise it is utilised in sediment transport analysis in open channels. Part II addresses the study of river engineering related to the unsteady changes in the longitudinal direction. Hence the theory of flood routing is briefly discussed. Simplified models based on the diffusion analogy are adopted for one-dimensional flood routing analysis. The finite element method is applied in the formulation of a variable parameter diffusion model called RFRFEM for the solution to the nonlinear convection-diffusion equation. A detailed study of the routing parameters is performed based on the prediction of the rating curve. Model validation is attained through comparisons with,, both analytical solutions for simplified cases and systematic series of flood routing benchmark tests for inbank flow. It ultimately deals with the joint application of the turbulence and routing models to analyse overbank flood routing in natural rivers.