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We present a new method for modeling and design of photonic crystal nano-beam resonators (PCNBRs) based on cascaded transmission lines. The proposed model provides an accurate estimate of the PCNBRs properties such as resonance wavelength and quality factor (Q) with much smaller computation cost as compared to the brute-force numerical methods. Furthermore, we have developed a straightforward technique for the design of high-Q PCNBRs based on resonance modes with Gaussian electromagnetic field profiles. The results obtained by using the proposed transmission line model are compared against numerical and experimental results and the accuracy of the model is verified. The proposed model provides an insight to silicon cavity design and significantly reduces computational burden.