The deformation of cylinders made of elastic materials, either homogeneous or fiber-reinforced, at large deformations under the action of centrifugal forces was investigated by using equations of the complete model of axisymmetric deformation. Based on this model, particular features of the behavior of elastic cylinders, nonreinforced or reinforced with circumferential and radial systems of fibers, were examined. The deformation of cylinders with sliding and rigid fits on their inner surface was considered in free rotation. It is found that the deformation of the cylinders can be described by means of the model of plane deformation.