Abstarct: Tsunami numerical modeling was considered since tsunami in Indonesia in 2004.Shallow water equations are governing equations for tsunami propagation.First step in tsunami modeling is to create tsunami then the waves propagation can be modeled .In this report , numerical modeling is used to investigate tsunami propagation and inundation . Elastic fault plane theory is used to create tsunami. Linear shallow water equations in spherical coordinate are used to model tsunami propagation ; and nonlinear shallow water equations in cartesian coordinate are used to model tsunami inundation . To verify tsunami modeling , Japan 2011 tsunami data is applied. Tsunami inundation in eastern coast of USA is being modeled and the results are shown as inundation map of the area . Using the results of this thesis can reduce the destruction of coasts, so important buildings can be constructed in low danger areas .