Results of a numerical simulation of the action of distant tsunamis on the coast of the Russian Far East are presented. It is shown that waves generated by focuses of the strongest M9 earthquakes in the region of South Chilean coast, as well as in the region of Papua New Guinea and Solomon Islands, are most dangerous for this coast. Other tsunamigenic zones of the Pacific Ocean, by virtue of their geographical position, orientation of focuses, and absence of pronounced channels (submarine ridges) along paths of tsunami propagation are not dangerous for it even at a limit magnitude of submarine subduction earthquakes. The simulation results are compared with historical data about manifestations of distant tsunamis on the Russian Far East coast.