Abstract: The causes and the characteristics of the tsunamis are briefly reviewed，the factors which affect earthquake-generated tsunamis analyzed, and the physical basis of tsunami early warning is presented. Taking the great Sumatra－Andaman earthquake of December 26, 2004 (MW9.0) and the great Northern Sumatra earthquake of March 28, 2005 (MW8.7) as examples, it is shown that the moment magnitude or its equivalent, seismic moment, source mechanism, focal depth as well as earthquake rupture process are major factors which play important roles in the tsunami generation process. A comparison between the 2004 great Sumatra－Andaman earthquake and the 2005 great Northern Sumatra earthquake is made to explore the characteristics of the tsunamigenic earthquake and to emphasize the urgent need of studies on the characteristics and mechanism of tsunamigenic earthquake for prevention and mitigation of tsunami disaster.