Cover Caption: A velocity-based space–time finite element method (v-ST/FEM) is presented for analyzing dynamic soil–structure interaction in earth structures such as dams, tunnels, and embankments subjected to vibrational loading from high-speed trains, road traffic, underground explosions, and earthquakes. The method incorporates the Lysmer–Kuhlemeyer viscous boundary conditions to truncate the unbounded soil domain and includes time-dependent boundary conditions to model energy flow. The v-ST/FEM is third-order accurate in time. It introduces negligible numerical dispersion error, thus enabling precise computation of the dynamic responses of soils and structures during long-duration earthquake motions.