This thesis focuses on numerical modeling of depth-averaged shallow water equations. The finite volume based shock-capturing methods are used to discretize the governing equations. The one-dimensional and two-dimensional equations are solved implicitly using Newton-Raphson method for each time step. The two-dimensional model is implemented on unstructured quadrilateral as well as triangular grids. Applications and accuracy of the models are investigated using the experimental data and the previous numerical results available in the literature. The models are also validated by simulating tidal variations in a small stretch of the River Hooghly, India. A coupled model is also demonstrated and tested. In this approach, the river flow is considered to be one-dimensional and the floodplain flow as quasi two-dimensional. The two models are coupled considering only the mass flux and neglecting the momentum flux. The coupled model is applied to a small reach of River Thames, UK to predict the extent of inundation due to a real flood event and the results are compared with that derived from satellite imagery.