The maximum safe operating speed or flywheels and shafts made of low tensile strength material is often determined by the speed at which radial tensile stress exceeds a radial tensile stress limit for the material. Circumferentially wound fiber composite material, for example, has a relatively low tensile strength along the radial direction perpendicular to the fibers. To increase the maximum safe operating speed, it is therefore desirable to form a fiber composite flywheel or shaft with radial compressive prestress. Such a prestressed flywheel or shaft has an outer annulus and an inner cylinder disposed in the outer annulus, and an annular layer of solidified bonding agent within an annular region between the outer annulus and the inner cylinder, wherein the outer annulus and the inner cylinder include substantial radial prestress induced by the bonding agent. The rim portion of a flywheel, for example, is formed from an outer ring (the annulus) and an inner ring (the cylinder, which is hollow in this case). Large, thick flywheels preferably have multiple cylindrical sections joined by such layers of bonding agent, and a plurality of the cylindrical sections each including an outer layer of relatively stiff fiber-composite material, and an inner layer of relatively compliant fiber-composite material within an integral matrix material.