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This chapter establishes the relationship among earthquake source parameters and the generation, propagation, and run-up of local tsunamis. In general terms, displacement of the seafloor during the earthquake rupture is modeled using the elastic dislocation theory for which the displacement field is dependent on the slip distribution, fault geometry, and the elastic response and properties of the medium. Specifically, nonlinear long-wave theory governs the propagation and run-up of tsunamis. A parametric study is devised to examine the relative importance of individual earthquake source parameters on local tsunamis, because the physics that describes tsunamis from generation through run-up is complex. Analysis of the source parameters of various tsunamigenic earthquakes have indicated that the details of the earthquake source, namely, nonuniform distribution of slip along the fault plane, have a significant effect on the local tsunami run-up. Numerical methods have been developed to address the realistic bathymetric and shoreline conditions. The accuracy of determining the run-up on shore is directly dependent on the source parameters of the earthquake, which provide the initial conditions used for the hydrodynamic models.