Most　transoceanic　tsunamis　are　destructive,　such　as　1960　Chile　tsunami　and　2004　Sumatra　tsunami.　The　propagation　mechanisms　of　transoceanic　tsunami　and　near-field　tsunami　are　different,　so　are　the　mathematical　mod-els.　In　this　paper,　based　on　the　finite　difference　method,　the　leap-frog　scheme　is　used　to　solve　the　linear　shallow　e-quations　by　comparing　with　Boussinesq　equations.　As　an　example,　2004　Sumatra　tsunami　is　simulated,　and　the　cal-culation　results　are　compared　with　those　provided　by　NOAA　and　NGDC.　The　methodology　suggested　in　this　paper　will　give　the　technological　support　to　the　tsunami　hazard　analysis　and　the　tsunami　warning　service.