Folklore tells of a large sea wave that struck an area of Chenggong on the eastern coast of Taiwan. This event is estimated to have occurred in the middle of the 19^th century based on an oral history of the area. Despite an estimated run-up height of more than 18 m, no other folklore related to a tsunami has been found in areas adjacent to the site for several reasons. Considering the importance of understanding the dangers posed to the eastern coast of Taiwan, numerical tsunami simulations were carried out to study localized amplification effects. Three tsunami sources were studied: (1) the westernmost portion of the Ryukyu trench, (2) offshore of Chenggong and (3) the source of the 1771 Yaeyama tsunami along the Ryukyu trench. Numerical simulations using detailed bathymetric maps reveal that possible tsunami waves are not significantly amplified around Chenggong; the eastern coast of Taiwan should have been affected by the 19^th century tsunami if it was large enough. This study emphasizes the importance of investigation of paleo-tsunamis along the eastern coast of Taiwan to assess the risk for future tsunami hazards.