SOI-based micro-ring resonators can be ultra-compact and highly sensitive for sensing applications. In order to obtain deeper notches and enlarge the detection area, the concentric double-ring resonators have been proposed. To further increase the sensing area and promote the sensing sensitivity, we add one more inner ring into the double-ring structure to form the triple-ring resonator. In this thesis, we have derived the transfer functions of the multi-ring structures and calculated the resonance properties of the triple-ring resonators by using the 3-D FDTD method. We have investigated the effects of the ring radius on the transmission spectra and discussed the variations of spectral response between the double-ring and triple-ring resonators. We also demonstrate the applications of the triple-ring resonator as the refractive index sensors. The triple-ring resonator can obtain deeper dips and higher detection sensitivity of 12.85 nm/RIU. Enlarging the gap can increase the sensing area and is shown to be able to promote the sensing sensitivity. Besides, the influences of the light polarization and the optical absorption on the spectral responses have been discussed as well.