The June 15, 1896 Sanriku earthquake generated devastating tsunamis with the maximum run-up of 25 m and caused the worst tsunami disaster in the history of Japan, despite its moderate surface wave magnitude (MS=7.2) and weak seismic intensity. This is a typical tsunami earthquake, which generates anomalously larger tsunamis than expected from its seismic waves. Previously proposed mechanisms of tsunami earthquakes include submarine slumping and slow rupture in the accretionary wedge or in the subducted sediments. In this paper, we estimate the fault parameters of the 1896 tsunami earthquake by numerically computing the tsunami and comparing the waveforms with those recorded at three tide gauge stations in Japan. The result indicates that the tsunami source is very close to the Japan trench and the fault strike is parallel to the trench axis. The fault width is about 50 km, suggesting that the tsunami earthquake is a slow rupture in the subducted sediments beneath the accretionary wedge. ¿ American Geophysical Union 1996