A helmet for protection against non-motorized injuries comprises a number of arched segments with ventilation spaces between them, the arched segments being shaped to extend about and engage the skull. The helmet is constructed to cover the apical as well as the frontal, temporal and occipital basilar skull. The arched segments are convex on their outer surfaces, have flat, curved inner surfaces, and are made of a cushioning, impact absorbing material such as plastic foam. Reinforcing elements extend in longitudinal passages in the arched segments to provide resistance against forces which are only partly absorbed by the cushioning material. In an alternate embodiment, support straps extend over the apical skull, and an impact resistant helmet is worn over the apical skull.