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Most existing arch dams have been designed for seismic loading by static methods involving the use of seismic coefficients. Although there are no known examples of arch dams which have been seriously damaged by earthquakes, the need for more realistic seismic analyses is now well recognized, not only for new dams but especially in the context of the safety evaluation of existing dams. Fortunately, with the finite element method, engineers have a powerful tool for modeling the complex geometry and the nonlinear material behavior of a dam. However, there is still a major complication in the analysis procedure, namely the interaction of the dam with the reservoir and with the foundation during an earthquake. Interaction is a wave propagation problem involving transmitting boundaries. The State of the Art in engineering practice is to neglect wave propagation by modeling the water as incompressible and the foundation as massless. More advanced analysis methods using compressible water and foundation with mass have been available for some time. However, these methods are restricted to linear models, because they work in the frequency domain. On the other hand, there are also advanced nonlinear models for dams, but they can only be used in the time domain, usually with simple transmitting boundaries. In this report, which is based on an a doctoral thesis, rigorous transmitting boundaries in the time domain are developed which permit combining compressible water with n- linear dam behavior. The new numerical model is based on a systems-theory approach.