Abstract: A safety helmet for e.g. motorcycles has its outer shell firmed as a sandwich, comprising outer and inner composite layers each of resin and impact-resistant material separated by an intermediate layer of resilient material. The impact-resistant material is preferably a cloth of high tensile strength fiber such as KEVLAR.TM., DYNEMA.TM., glass fiber, or carbon fiber. The resilient material may be cork or foamed or other resilient plastics material, but is preferably honeycomb material of paper or aluminum. The helmet is made by sequentially laying up, in or over a former, a first composite layer of resin and sheets of impact-resistant material, an intermediate layer of honeycomb material, and a second composite layer of resin and sheets of impact-resistant material. The outer shell has a polyhedral form including a plurality of polygonal faces having abutting edges.