Dose rates of gamma rays from a 60Co cylindrical source surrounded coaxially by a cylindrical shield were measured in the radial direction in a plane passing through the midpoint of the axis of the source. The 60Co was uniformly distributed in a water-like medium. The shield was composed of water and iron, each in a single layer, and of water and iron in a double layer. The concept of the dose buildup factor for a volume source was introduced and the behavior of gamma rays scattered from the shielded cylindrical source was considered. The variation of the dose buildup factor for the shielded cylindrical source as a function of the distance from the source is less than the variation for the unshielded source. The dose buildup factor for a cylindrical source, with and without shields, shows many features that differ from those generally observed, i.e., an infinite medium surrounding a point source and one obtained from the total gamma-ray dose rates calculated by integration of an attenuation kernel with dose buildup factors for a point isotropic source. The unique behavior of the dose buildup factor for the cylindrical source with a cylindrical shield is shown by supplemental experiments with a 60Co point source to be due to the cylindrical shape of the source and shields.