The thesis quantifies the peak ground acceleration (PGA) required to cause large rock avalanches in the western rangefront of the Southern Alps in New Zealand, which will improve understanding of the hazard posed by co-seismic landslides in the West Coast region. During an earthquake, ground motion can destabilize both man-made and natural structures. The Alpine Fault, which runs along the western edge of the Southern Alps and forms part of the boundary between the Australian and Pacific Plates, is a seismically active fault which appears to be in the late phase of its earthquake cycle, and a major earthquake (Mw $\geq$ 8) is expected in the near future. Seismic events are known to cause landslides in many regions of the world and are thought to be responsible for a series of large rock avalanches in New Zealand. Since large earthquake-triggered landslides often have anomalously long runouts and can induce tertiary hazards through dam breaking and subsequent flooding, they have substantial hazard potential. The thesis quantifies the strength of PGA required to trigger large rock avalanches in the western rangefront of the Southern Alps, using published data on two particular potentially co-seismic landslides: The Round Top rock avalanche, and the Cascade rock avalanche. Newmark’s sliding block model, a permanent-displacement analysis which models a landslide as a rigid block sliding down an inclined plane, is, with some modifications introduced in this work, used to estimate the strength of PGA required to initiate these landslides. 2D static slope stability analyses are conducted using 9m and 15m resolution DEMs of the landslides, providing estimates of the Factor of Safety (the ratio between resisting and driving forces), which is then used to estimate the required strength of PGA. The results show a median estimated lower-boundary PGA for the Cascade rock avalanche of 0.85g, with a margin of error of -0.14/+0.15 (0.71g-1g). The corresponding result for the Round Top rock avalanche is 0.92g, with a margin of error of $ \pm $0.25 (0.67-1.17g). The predicted PGAs derived from these landslides will be potentially useful for constraining scenario ground motions for future Alpine Fault earthquakes.