A time-dependent two-dimensional numerical model was developed to study the generation and propagation of a tsunami resulting from a major earthquake predicted to occur in the Shumagin Seismic Gap area of the eastern part of the Aleutian Island chain. The grid size is approximately 28 km in the latitudinal direction and 36 km in the longitudinal direction. The leading wave of the tsunami took only about three hours to arrive at the southern Britich Columbia coast and the northern part of the coast of the state of Washington. On the other hand, it took about eight hours to propagate into the Bering Sea. Two important results emerged from this study. The tsunami waves show very strong directionality, and the presence of the so-called lateral waves can be inferred. In the deep ocean, tsunami amplitudes up to one meter appear to occur. To deduce the detailed distribution of the tsunami amplitudes at the coast, the present large area model has to be coupled to a coastal model which uses either finer rectangular grids or irregular triangular grids.