A systematic investigation of the dynamic behavior of Ni${}_{80}$Fe${}_{20}$ ring arrays using broadband ferromagnetic resonance spectroscopy as a function of inter-ring spacing and ring thickness is presented. Four distinct resonance modes were found for rectangular rings compared to the two modes seen in circular rings of identical width due to the presence of sharp corners and nonuniform demagnetization field distribution. The resonance peaks were sensitive to the inter-ring spacing and the ring thickness due to magnetostatic coupling. Micromagnetic simulations and analytical calculations are compared with the experiment results.