The hydrodynamic and mathematical problems connected with discontinuity between wet and dry domains, nonlinearity, friction, and computational instability are the main problems that have to be sorted out in the runup computation. A variety of runup models are analyzed, including the boundary conditions used to move the shoreline. Based on the initial experiments one‐dimensional and two‐dimensional algorithms are constructed. These models are tested against analytical solutions obtained by others. The extent of inundation along Alaska, British Columbia, Washington, and Oregon coasts caused by the 1964 Alaska earthquake tsunami is well documented. The data gathered at Alberni Inlet, British Columbia, Canada, is used to test the numerical model and the boundary conditions set at the mouth of the inlet. The computed extent of flooding turned out to be in satisfactory agreement with the data obtained from the observations.
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