A parallel finite difference numerical simulation program based on the Navier-Stokes (NS) equations is developed for simulating 3-D tsunami generation and propagation. We can simulate tsunami propagation over more than 1000 km using this program, although such tsunami propagation over long distances has usually been conducted on the basis of on 2-D simulations. Some 2-D simulations have assumed that the initial tsunami distribution is identical to the sea bottom deformation caused by the earthquake. The 3-D simulations, however, indicate that this assumption is inappropriate when the source width 2a _x is less than 10 times the sea depth h (2a _x < 10h) for a source process time of 20 s. Dispersion of tsunami appears when the source is of small size, and the dispersion is more apparent in a direction perpendicular to the fault strike. We also conduct tsunami simulations for two intraplate events: the 2004 off–Kii Peninsula (M 7.4) and the 2007 off–Kuril Islands (M 8.1) events. The 3-D tsunami simulation has successfully simulated the offshore tsunami, and we obtained good agreement between the observations and the calculations for both events. In particular, for the 2004 off–Kii Peninsula event, although the 2-D linear long-wave theory cannot simulate important characteristics in the record such as the arrival time of the peak amplitude and the dispersive tsunami, the 3-D NS simulation is well able to model those characteristics.