The problem of fracture initiation within the vicinity of elastic/plastic indentations is examined. The fractures are considered to originate from one of two sources: preexistent flaws (such as surface cracks formed during mechanical finishing) or stress singularities created by shear bands. The initiation of radial cracks from preexistent flaws has been predicted and shown to correlate quite successfully with threshold data obtained using a range of brittle solids. The trends in fracture initiation associated with the existence of a nucleation step (as appropriate for many median and lateral cracks) are also discussed.