Tsunami are long water waves generated by sudden disturbances of the sea floor or sea water surface, which is usually caused by earthquakes, landslides or volcanic eruptions. Once triggered the tsunami can propagate over long distances, carrying destruction even on far coasts, hours after the impulsive generating event. The tragic consequences of the tsunami occurred the 26th December 2004 in the Indian Ocean, involved the scientific community to develop models able to reproduce the tsunami generation and their evolution, with the aim of building Tsunami Early Warning Systems. A single model is not able to treat adequately the generation, propagation and inundation phase of tsunami scenarios, because it can not be at the same time accurate and computational efficient. The tsunami generation most of the times requires the solution of the full three dimensional equations of the hydrodynamics (Grilli et al., 2002; Liu et al., 2005), in order to accurately reproduce the complex sea floor motion and therefore the consequent wave field. A mathematical problem which solves the three dimensional equations is especially needed when tsunami are generated by landslides or small submarine earthquakes. An other important feature which has to be taken into account when modelling the tsunami generation, are the nonlinear terms, which allow the reproduction of waves with a wave height of the same order of the water depth. The nonlinear equations have to be solved when the generating seismic event occurs close to the coast in shallow water, which represents the most dangerous threat for people and structures. When the tsunami propagates far from the generating source it can reach high celerity, of the order of thousands of m/s. Tsunamis in deep water are long waves (wave length of the order of hundreds kilometres) with wave height of the order of one meter; therefore, if compared to the water depth (thousands of metres), can be considered small amplitude water waves. The tsunami propagation phase can therefore be accurately modelled using linear equations. When the wave propagation is to be studied over large geographical areas it appears natural to apply simplified equations in order to reduce the computational costs. These are the depth-integrated equations which reduce the full three-dimensional problem to a two-dimensional one, making the resulting model applicable over oceanic length scales. The most widely equations used are the long wave equations, named also Nonlinear Shallow Water Equations (NSWE). One weak point of the NSWE is that they are not able to reproduce properly the celerity at which each component of the wave field propagates.