A study is made of seismic wave propagation at the edge of sedimentary basins and valleys, and the subsequent amplification of earthquake shaking that occurs. The aim of this thesis is to determine the geological and seismic conditions that control the occurrence and nature of basin-edge effects. In the first half of the thesis, elastic SH-wave propagation is investigated at the edge of a two-dimensional semi-infinite homogeneous layer above a homogeneous half-space, first with a geometrical ray-path and wavefront analysis and then with finite-element modelling of plane incident Ricker wavelets. It is shown that Love waves generated at an edge produce characteristic patterns of amplification across the layer in both the time and frequency domains. In addition, occurrences of localised amplification at the edge of the layer are categorised into three different classes based on their mechanisms of development. The Airy-phase edge effect occurs when the input frequency is close to the fundamental frequency of the layer; the wedge effect occurs above shallow sloping edges; and the basin-edge effect occurs above deep basins adjacent to steeply dipping edges. The second half of the thesis makes a case study of seismic amplification and edge effects in the Lower Hutt Valley. It is found that the anti-plane seismic response is characterised by multi-dimensional resonance across the full width, and the basin-edge effect and strong differential motion adjacent to the vertically-dipping Wellington fault. Love waves generated at each edge are the primary cause of such spatially varying ground motions. Modelling results are compared with an analysis of weak ground motions recorded on a dense linear array of instruments across the fault-bounded edge of the valley. A high degree of similarity is found. Discussion is also made concerning the use of the twodimensional elastic SH-wave analysis for predicting seismic response during strong ground shaking.