Two input models of seismic excitation, the nonlinear contact characteristics of contraction joints, were presented. The influence of the damping ratio on the seismic response of a high arch dam was then investigated. A new element (the viscous-spring boundary element capable of reflecting the radiation damping effects of an infinite foundation), the external source wave input subroutine, and the dynamic contact models, including the characteristics of normal opening-closing and radial sliding, were developed in this paper. The nonlinear contact behavior of contraction joints was simulated using a nonlinear exponential dynamic contact model, and the radial nonlinear characteristic was simulated using the Mohr-Coulomb criterion. Linear elastic and nonlinear seismic response analyses for a 300-m high concrete arch dam under construction were performed. The results showed that the damping ratio greatly influenced the seismic response of a high arch dam using a massless foundation model, and the damping ratio between 3–5% resulted in a conservative seismic response. The results of the viscous-spring boundary input model were in good agreement with those given by the massless foundation model when a damping ratio of 10% was used, but the openings of joints near the crown cantilever varied significantly. The effects of radiation damping of the foundation on the seismic response could be simplified to some extent by increasing the material damping of the dam in this study.