This thesis uses numerical simulations to assess the most suitable model type for simulating dispersive and non dispersive tsunami wave propagation over a range of bathymetries. These simulations are presented in two parts. The first part highlights differences between results as predicted by a fully nonlinear Boussinesq model (with its ability to predict dispersion) and a non dispersive, linear or weakly nonlinear model, for simulations of a dispersive wave incident at various idealized bathymetric features. The second part determines the efficacy in a real world application of the Boussinesq model as opposed to a nonlinear shallow water model. In addition, a discussion on the geophysical parameters which influence the choice of numerical model for simulating tsunami propagation in a particular bathymetric region is provided.