A skeletal dome structure composed of a plurality of arcuate support beams joined at their upper ends to a central hub and radiating outwardly and downwardly to terminate at points of engagement with a support surface. Each support beam is composed of an elongated lightweight core sandwiched between upper and lower strips of a material having high tensile and compressive strength. In making the dome, each beam is first preassembled to the extent that the core thereof is secured to a first strip, that strip is then attached at one end to the central hub, the first strip and core are then longitudinally flexed to develop a convex curvature along the side of the core opposite from the strip, and a second flexible strip is then secured to the convex side of the core. A plurality of such beams may be simultaneously formed into buckled or arcuate shape by connecting a plurality of the first strips to a single hub and then raising the hub to impart a curvature into each of the partially-finished beams, followed by the final step of securing the outer strips or skins to the convex upper surfaces of all of the outwardly-radiating arcuate members.