Three-dimensional simulation has become an indispensable approach to develop improved understanding of ring rolling technology, with validity as the basic requirement of the ring rolling simulation. Cold ring rolling is simple conceptually, however complex to analyze as the metal forming process is subject to coupled effects with multiple influencing factors such as sizes of rolls and ring blank, form geometry, material, process parameters, and frictional effects. Investigating the coupled thermal and plastic deformation behavior (the plastic deformation state and its development) in the deformation zone during the process is significant for predicting metal flow in order to control the geometric and tensile residual stress quality of deformed rings, and to provide for cycle time optimization of the cold ring rolling process. In this work, we present derivation of a 2-D analytical description governing ring rolling under the plane strain assumption, then perform finite element analysis of the same process from a surrogate flat rolling condition, extended to 3-D ring rolling. The analytic model reduction is shown to be acceptable for rough process parameter setting, and the finite element analysis can be used to tune the manufacturing process for cycle time optimization.