We simulate the optical fields and optical transmission through nanoarrays of silica rings embedded in thin gold films using the finite-difference-time-domain (FDTD) method. By examining the optical transmission spectra for varying ring geometries we uncover large enhancements in the transmission at wavelengths much longer than the usual cutoffs for cylindrical apertures or where surface plasmons or other periodic effects from the array could play a role. We attribute these enhancements to closely coupled cylindrical surface plasmons on the inner and outer surfaces of the rings, and this coupling is more efficient as the inner and outer ring radii approach each other. We confirm this hypothesis by comparing the transmission peaks of the simulation with those deduced from cylindrical surface plasmon (CSP) dispersion curves obtained from a normal mode analysis. These theoretical peak positions and their dependence on the ring geometry are in close agreement with the simulations. The behavior of the CSP dispersion is such that propagating modes can be sent through the rings for ever longer wavelengths as the ring radii approach, whereas the transmission decreases only in proportion to the ring area.