Gigantic submarine landslides are among the most energetic events on the Earth surface. During the Late Pleistocene the Mediterranean Sea was the scenario of a 9 number of such events, some of whose geological fi ngerprints are the 500 km 3 mass transport deposit SL2 at the Nile delta fan (dated at ca. 110 ka BP) and the Herodotus Basing Megaturbidite (HBM, a 400 km 3 deposit dated at ca. 27.1 ka BP). This paper presents an exploratory study on the tsunamigenic potential of these slides by using a numerical model based on the 2D depth-averaged non-linear barotropic shallow water equations. The sliding mass is modelled both as a rigid block with a prescribed motion and as a viscous fl ow layer. The 26 km 3 debris fl ow BIG'95 scenario (at the Ebro continental slope, 11.5 ka BP) served for model com-parison against independent modelling works. Based upon the available geologicalstudies, several source scenarios have been modelled. Our results show that the generated tsunamis would have had up to hundred fold the peak energy of some extreme historical ones, such as the 1755 Lisbon tsunami. Thus, the HBM tsunami could have reached peak energies over one hundred Megatons, producing runups over 50 m height along some 1300 km 2 of shoreline in the eastern Mediterranean.The study also comprises their propagation pattern, their impacts along the former shoreline and their energy partitioning. The highest tsunami energies were associated to thick landslides at shallow depths, with high slope angles and within a gulf geometry.