Scenarios represent a very useful technique for the definition and evaluation of tsunami hazard and risk for any given region, and a basic step in the frame of tsunami mitigation and preparedness and of sustainable coastal zone development. With the exception of very few countries, like Japan and the United States, emergency plans in the rest of the world have never taken serious care of tsunamis until the occurrence of the giant Indian Ocean tsunami on December 26, 2004. That event dramatically brought the problem of tsunami hazard and risk assessment to the general attention and showed the urgent need for implementation of tsunami early warning systems (TEWSs). The problem is particularly urgent for the Mediterranean countries that are known to have been attacked by numerous tsunamis in the past, several of which had catastrophic size and impact. This paper is an attempt to develop some simple scenarios of earthquake-generated tsunamis in the Mediterranean. We identify four different seismogenic areas in the western, central and eastern sectors of the basin. For each of them, we take into account a seismic fault capable of generating an earthquake with magnitude equal or larger than the highest magnitude registered in that region in historical times. Then we simulate numerically the ensuing tsunamis, highlighting the basic features of the wave propagation and roughly identifying the coastal sectors that are expected to suffer the heaviest tsunami effects. One of the most important outcomes is that these scenario tsunamis attack the nearest coasts within at most 15 minutes, which poses serious constraints for designing appropriate TEWS for the Mediterranean.