A complete model of a soil-foundation-structure system for use in response history analysis requires modification of input motions relative to those in the free-field to account for kinematic interaction effects, foundation springs and dashpots to represent foundation-soil impedance, and a structural model. The recently completed ATC-83 project developed consistent guidelines for evaluation of kinematic interaction effects and foundation impedance for realistic conditions. We implement those procedures in seismic response history analyses for two instrumented buildings in California, one a 13-story concrete-moment frame building with two levels of basement and the other a 10-story concrete shear wall core building without embedment. We develop three-dimensional baseline models (MB) of the building and foundation systems (including SSI components) that are calibrated to reproduce observed responses from recorded earthquakes. SSI components considered in the MB model include horizontal and vertical springs and dashpots that represent the horizontal translation and rotational impedance, kinematic ground motion variations from embedment and base slab averaging, and ground motion variations over the embedment depth of basements. We then remove selected components of the MB models one at a time to evaluate their impact on engineering demand parameters (EDPs) such as inter-story drifts, story shear distributions, and floor accelerations. We find that a “bathtub” model that retains all features of the MB approach except for depth-variable motions provides for generally good above-ground superstructure responses, but biased demand assessments in subterranean levels. Other common approaches using a fixed-based representation can produce poor results.