A coupled numerical model based on the shallow-water equations is employed to simulate the Nihonkai-Chubu Earthquake Tsunami event which occurred in 1983. The model consists of a transoceanic propagation and an inundation model both described by finite difference methods. A special moving boundary treatment is implemented in the inundation model to track accurately a transient motion of shoreline. Maximum run-up heights along the Eastern Coastline of the Korean Peninsula are predicted and compared to field measurements. In particular, the maximum run-up height at the Ulchin Nuclear Power Plant is estimated and compared to the observed height to analyze the safety of the Plant. Although the numerical model slightly overestimates the maximum run-up heights, the model still provides reasonable predictions.