A novel approach using microresonating system with low power consumption is proposed for determining Young's modulus of mirco and nano-sized waveguide material. Based on the Mason rule with signal flow graph (SFG) method in the Z-domain, the optical transfer function is derived for resonating layout consists of two single microring resonators which are indirectly coupled to an add-drop micro resonator. A mathematical function is determined for critical coupling coefficient and the optimum optical transmission of proposed system. For the resonant mode numbers of 5;3;3, the free spectral range (FSR) is extended to 182 nm with the out of band rejection ratio(OBRR) of 50 dB and the Q factor is 8593. The Young's modulus is determined based on a change in the sensing ring radius due to the applied external force on the waveguide that causes the wavelength shift in resonant peaks. The Young's modulus for the lateral surface of the SOI waveguide with 250 nm height and 1.5 mu m radius is determined to be 147.72 GPa and for the upper surface of the SOI waveguide with 440 nm average width and 1.5 mu m radius is determined to be 83.93 GPa. The proposed resonating system is a potential candidate for measuring Young's modulus of materials in mirco and nano size with high resolution and has the advantages of the low power consumption due to the low intensity source.