Various optical functional devices with multiple paths are studied. We have also studied the chracteristics of a double ring optical resonator as an optical functional device with multiple paths. In the double ring resonator, the difference of the propagation time exists between an inner ring and an outer ring. Therefore, we propose the analysis method in consideration of propagation delay time. This method was applied to our double ring resonator. It turns out that it is valid. In addition, the modulation analysis for double ring modulator was also performed with this method.