A ring resonator composed of a plasmonic waveguide is presented. For the plasmonic waveguide, an array of silver nanorods is assumed. To determine the modes of this ring resonator, the generalized multipole technique (GMT) is used. Using this analysis, we obtain various modes of the proposed ring resonator. The mode field and the corresponding quality factor of each mode of the ring resonator is computed. The results are compared with those obtained using the finite-element method (FEM) and the finite-difference time domain (FDTD) method.