Abstract: Bulk (RE)BCO, where RE is a rare-earth element or yttrium, superconductors fabricated in the form of rings are potentially useful for a variety of solenoidal-type applications, such as small, high field nuclear magnetic resonance and electromagnetic undulators. It is anticipated that the practical exploitation of these technologically important materials will involve pulse field magnetization (PFM) and, consequently, it is important to understand the behavior of ring-shaped samples subjected to the PFM process. Macroscopic flux jumps were observed in PFM experiments on ring-shaped bulk samples when the peak applied field reaches a threshold magnitude, similar to behavior reported previously in cylindrical samples. Magnetic flux jumps inward when the thermal instability is triggered, however it subsequently flows outwards from the sample, resulting in a relatively low trapped field. This behavior is attributed to a variety of effects, including the inhomogeneity of the material, which may lead to the formation of localized hot spots during the PFM process. In order to further elucidate this phenomena, the properties of a structure consisting of a bulk superconducting ring with a cylindrical superconductor core were studied. We observe that, although a flux jump occurs consistently in the ring, a critical state is established at the boundary of the ring-shaped sample and the core. We provide a detailed account of these experimental observations and provide an explanation in terms of the current understanding of the PFM process.