The 1771 Meiwa Tsunami, which was generated on 24 April 1771, struck the Miyako-Yaeyama Islands located in the southern part of the Ryukyu Islands, Japan. It was one of the most devastating tsunamis ever to hit Japan. Based on historical documents and recent field surveys, the run-up heights at some areas of the Miyako-Yaeyama Islands were estimated as up to 30 m at Ishigaki Island, although it is noteworthy that the extremely high run-up heights were only observed at the southeastern coast of the island and those in other areas were generally lower than 10-15 m. Based on these run-up heights, several tsunami source models have been proposed. However, the model remains controversial because the actual fault, the putative tsunami source, has not been identified. For this study, we conducted numerical calculations to test the tsunami source models. We used reliable observed run-up heights including newly available data around the Miyako Islands as well as the high-resolution bathymetric data with reef topography. By comparing estimated and calculated run-up heights, we tested the validity of the previously proposed models as well as that of our own. Results showed that the tsunami generated by the reverse dip-slip intraplate fault plus the subsequent occurrence of a submarine landslide offshore from southeastern Ishigaki Island is the preferred model because it reproduces the historically documented run-up heights well. In particular, this model explains unusually high run-up heights at the southeastern coast of Ishigaki Island as a result of the local effect of the submarine landslide. Possible evidence of some landslides has been found in this area, but a detailed submarine survey is necessary to confirm the source model and to find evidence of the submarine landslide generated by the 1771 earthquake.