A review of the observations of indentation‐induced fracture suggests that there is no simple generalization which may be made concerning crack initiation sequences. Here, we investigate the material dependence of the initiation sequence of indentation cracks (cone, radial, median, half‐penny, and lateral) using an inverted tester allowing simultaneous viewing of the fracture process and measurement of the indeter load and displacement during contact. Two normal glasses, two anomalous glasses, and seven crystalline materials are examined. Key results include (i) direct evidence that the surface traces of cracks observed at indentation contacts are those of radial cracks, rather than median‐nucleated half‐penny cracks (at least for peak contact loads <40 N) and (ii) that, in crystalline materials, radial cracks form almost immediately on loading of the indenter, in anomalous glasses at somewhat greater loads, but in normal glasses during unloading. A detailed consideration of the stress fields arising during indentation contact predicts material‐dependent initiation sequences, in agreement with observations, particularly those of radial crack formation on loading for materials with large modulus‐to‐hardness ratios. In addition, a new, unexplored crack system is demonstrated, the shallow lateral cracks, which appear to be responsible for material removal at sharp contacts.