Polygon resonators are promising candidates for nanomechanical applications due to their compact architecture and high force sensitivity. Here, we develop a polygon-specific analytical model for perimeter modes by coupling the flexural motion of the polygon sides to tether torsion governed by a stress-modified Timoshenko-Gere equation. The model captures finite-wavelength torsional phase accumulation beyond the conventional short-tether approximation, revealing tether-length-dependent resonances and bending-torsion hybridization. Comparisons with finite-element-method simulations show good agreement in the quasi-one-dimensional regime, while identifying the onset of deviations associated with neglected torsional deformation of the polygon sides. The model therefore provides a useful analytical tool for interpreting and optimizing high-quality-factor ($Q$) polygon resonators for cavity optomechanics and precision sensing.

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• Optomechanics