Numerical model to represent adequately a shallow water and bay region together with an open sea is constructed without an extreme increase of a number of grids. The computed values in this numerical model may be directly compared with data which are observed by a tide gage at the inside of a bay. As for the 1968 Hyuganada Earthquake, numerical experiments with the tsunami source computed from the dislocation of the earthquake fault are tried. The source model modified by about 10 degrees the dip angle of fault plane is fitter for the observed tsunami data than the one derived directly from seismic data. This model can reproduce the tsunami waves at 5 tide-gage stations in the error of ±20% in the height of the first crest of computed waves and of ±0.8min in the arrival time. The amplitude variation and the directivity of tsunami propagation, and the applicability of Green's law are examined. At the district of Hososhima, tsunami data are obtained at 3 sites, and it is found that the present numerical model is quite reliable to reproduce the variation of tsunami within a short distance.