In the study of the tsunami propagation phenomenon is very important to model the wave frequency dispersion because of its significant role during wave transformation from deep to intermediate waters. During the propagation to the shore, dispersive waves refract, shoal, due to coastal bathymetry morphology. Long waves have an high impact on surf-zone dynamics, sediment transport and beach erosion. In the Mediterranean sea, the effects of tsunamis on the coasts could be similar to the effects of large storms [

1,

2] and the detailed modeling of the shoreline movement is important in order to avoid big uncertainties [

3]. Tsunamis are huge waves generated by earthquakes, submarine volcanic eruptions or landslides. In very deep oceanic waters tsunami do not dramatically increase in height. But as the waves travel onshore, they increase in height as the bathymetry gradually decrease, becoming potentially destructive (e.g., the tsunami in Indian Ocean in December 2004, or in Japan in March 2011). Usually the tsunami were modelled as solitary waves and obliviously the shoaling, breaking, and run-up are phenoma of major interest for researcher [

4,

5,

6,

7,

8,

9]. The high computational power of modern computers and parallel computing make it possible to solve more and more complex fluid dynamics problems. Indeed, it is possible to solve 3D Reynolds Averaged Navier–Stokes (RANS) equations and use methods like Smoothed Particle Hydrodynamics (SPH) or Volume Of Fluids (VOF) [

10,

11,

12]. Unfortunately, 3D tsunami modeling requires high computational efforts that are not consistent with practical purposes. To overcome this problem we used the weakly dispersive model described by [

4,

13]. This kind of approach, also called the non-hydrostatic Non Linear Shallow Water Equations (NLSWE) method, usually solves, in the horizontal coordinates and time, free surface motion with a single value function. This requires a much lower vertical resolution than 3D methods. Moreover, the used model has an accurate modeling technique of wetting/drying processes [

4,

13]. The Western Ionian area, due to the clash between the African and Eurasian tectonic plates, is exposed to a high seismic risk causing possible tsunamis whose origin is directly related to earthquakes. In particular, the Greek and Italian (Calabrian and Sicilian ones) coastal areas are among the most exposed sites to such a hazard. These coastal areas, have a strong anthropization which makes them more vulnerable [

14]. In order to plan actions useful for risk mitigation, it is necessary to produce flooding and exposure maps that can be used for prevention and protection purposes. In the last decades, due to the recent tsunami disasters, researchers developed numerical models of increasingly quality. Ref Samaras et al. [

15], to simulate the effects of a tsunami striking the Greek and Sicilian coasts, used two-dimensional Boussinesq equations with a high order of approximation. Ref Schambach et al. [

16] used a non-hydrostatic three-dimensional model coupled with a non-linear and dispersive two-dimensional model to simulate the propagation of a tsunami on the coast, generated by the earthquake struck the city of Messina on 28th December 1908. Ref Mueller et al. [

17] used, instead, the well-known Cornell Multi-grid Coupled Tsunami model (COMCOT), which solves the NLSWE in spherical and Cartesian coordinates, to analyze the effects of scenarios of a flood near the Maltese coasts. The same two-dimensional model was adopted by [

18] to examine the characteristics of an earthquake-induced tsunami in the south of the province of Bali (Indonesia). In this paper, we present preliminary results regarding hypothetical strike of an earthquake induced tsunami on Sicilian coast. Furthermore, an inundation map, over a very small area, was produced by means of the weakly dispersive Boussinesq model [

4,

13].