An Efficient and Robust Tsunami Model on Unstructured Grids. Part I: Inundation Benchmarks. A modern multi-purpose baroclinic circulation model (SELFE) has been recently extended to include the ability to simulate tsunami propagation and inundation. The core model is based on the 3-D nonlinear shallow-water wave (NSW) equations, which are solved on unstructured grids, using the finite-element method. A semi-implicit method is used to solve all equations to enhance numerical stability, thus bypassing the most stringent CFL restriction on the time step. Further aided algorithmically by an Eulerian-Lagrangian solution of the advection terms in the momentum equation and by a simple yet effective inundation algorithm, SELFE is very efficient and robust in both quasi-2-D (with two vertical layers) and 3-D modes. A quasi-2-D version of the model is being used to update and expand the characterization of tsunami hazards along the Oregon coast. As a part of a rigorous testing procedure that includes multiple types of coastal problems, we present in this paper a quantitative assessment of performance of the quasi-2-D SELFE for two challenging open benchmark problems proposed in the 3rd International Workshop on Long-wave Runup Models. Satisfactory results are obtained for both problems.