The spatial variation of seismic ground motions has an important effect on the response of long structures (lifelines), such as pipelines, tunnels, dams and bridges. Because these structures extend over long distances parallel to the ground, their supports undergo different motions during an earthquake. Since the 1960’s, pioneering studies analyzed the inﬂuence of the spatial variation of the motions on above-ground and buried structures. At the time, the differential motions at the structures’ supports were attributed to the wave passage effect, i.e., it was considered that the ground motions propagate with a constant velocity on the ground surface without any change in their shape. The spatial variation of the motions was then described by the deterministic time delay required for the waveforms to reach the further-away supports of the structures. In these early studies, it was recognized that the consideration of inclined, rather than vertical, propagation of plane waves is beneﬁcial for the translational response of the large, mat, rigid foundations of nuclear power plants, induces seismic strains in buried pipelines and torsion in building structures, and affects the response of bridges.