Add to ORKGThe initial value problem of the linear evolution and runup of long waves on a plane beach is analyzed analytically. The shallow water-wave equations are solved by integral transform and eigenvalue expansion methodologies. The results from linear solutions are compared with the solution of the nonlinear shallow water-wave equations confirming the runup invariance, i.e. nonlinear and linear theories produce same maximum runup. Then, existing analytical nonlinear solution for shoreline motion is implemented for the waveforms given for near-shore earthquakes producing results exactly compared with existing ones, but with a much simpler algebra.Thesis (M.S.) -- Graduate School of Natural and Applied Sciences. Engineering Sciences