<p>On the basis of considering piezoelectric effect, high-order elastic coefficient, and geometric nonlinearity, this work establishes an initial stress model for rectangular quartz plates to calculate the force-frequency effect under axial force. Firstly, by perturbing the nonlinear equations caused by incremental deformation and linearizing the high-order incremental terms, the governing equations are derived. Subsequently, finite element method based model is derived with the consideration of nonlinear effect. The thickness-shear vibration frequencies and force-frequency relationships of the rectangular plates are obtained through eigenvalue analysis. From the results, it can be observed that the force-frequency relationship exhibits an approximately linear distribution under axial load in the present work. The force-frequency coefficient of the 19 MHz plate obtained by numerical calculation is relatively consistent with the experimental result, which verifies the accuracy of the proposed model. When the aspect ratio is greater than 3, the force-frequency relationship gradually stabilizes. The frequency shift of the plate with a fundamental frequency of 63 MHz is more sensitive to stress condition and dimensional size change, and the force-frequency coefficient is much higher. This work effectively solves the calculation problem of the force-frequency effect of quartz resonators considering nonlinear effects under initial stresses, providing an effective numerical calculation tool for the design of resonant force sensors.</p>