Multiprocessor interconnection networks can be built using a variety of topologies. Rings are one of the simplest and most effective topologies for parallel computers. This thesis uses the NUMAchine multiprocessor as a case study to explore the scalability and limitations of rings. The original NUMAchine interconnection network is built as a hierarchy of rings, where each ring has a maximum size of four nodes. A simulation study shows that a simple ring interconnect can support 32 or even 64 processors on a single ring. As a proof of concept, the NUMAchine hardware prototype is redesigned to use a single, expanded 32-processor ring. SPLASH-2 benchmarks running on the modified hardware demonstrate that a single ring is sufficiently scalable to support up to 32 processors for a multiprocessor such as NUMAchine.