This thesis has involved the development of an unstructured grid ocean model, H2Ocean, with accurate flooding and drying algorithms for tsunami studies. The research is co-funded by the Alfred Wegener Institute (AWI) in Bremerhaven, Germany, as part of their contribution to the German-Indonesian Tsunami Early Warning System, which is installed in Jakarta, Indonesia. The objectives are to improve the capability of the model in handling the flooding and drying, and dispersion. Based on an unstructured mesh finite element model TsunAWI, a finite volume model H2Ocean has been developed. This model is an analogue of the P1NC- P1 finite element. In the successful applications of the model in simulations of the 2004 Indian Ocean Tsunami and the 2011 Japan Tsunami, excellent agreement have been achieved, when compared to both flooding data and measured run-up. The model is found to be an accurate and efficient model for tsunami simulations.