The resonance properties of two-dimensional ring resonators consisted of the slot waveguide structure with throughput and drop ports and ring waveguides are numerically analyzed using the FDTD method. Polarization deals with TM waves that have components crossing the slot region. In the case of two-dimensional structures, the eigenmodes of slot waveguides can be analytically obtained, and these obtained eigenmodes are used as incident waves in the FDTD method. In numerical calculations, the influence of the radius of the ring waveguide, and the refractive index of the background medium on the resonant characteristics are investigated. Furthermore, sensitivity and FoM (figure of merit), which are important evaluation indices when using the ring resonator as a refractive index sensor, are also discussed.