Several different historical records allude to a disastrous tsunami on the southwestern Taiwan coast sometime between 1781 and 1782, with a reported death toll of more than 40,000. Despite consistent reports from southwest Taiwan no corroborative information exists for neighboring shorelines in southeast China or northwest Luzon, Philippines, and a plausible source of this tsunami has never been identified. Neither a large earthquake from the Manila trench and active thrust faults, nor a submarine volcanic eruption from the northern Luzon Arc can explain the very localized area affected and the physical phenomena described in the historical records. Comparing the results of 13 numerical models of tsunamis generated from different sources (earthquake, volcano and submarine-mass-failure), we therefore suggest that a seismically triggered, submarine-mass failure on the upper portion of the continental slope offshore from southwestern Taiwan is the most likely source of the 18th century event.