<p>This study developed an integrated numerical and data-driven framework for predicting the free-vibration characteristics of thin-walled curved box-girder bridges, a widely used yet mechanically complex structural form in modern bridge engineering. A computationally efficient one-dimensional thin-walled beam finite element method (FEM) was implemented in MATLAB, explicitly incorporating torsional, distortional, and warping effects, which are critical for accurately representing the dynamic behavior of curved girders. The proposed model was rigorously validated against detailed ANSYS shell-element simulations and published experimental data, demonstrating close agreement in both natural frequencies and corresponding mode shapes. A systematic parametric study was conducted to evaluate the influence of key design variables, including curvature radius, span length, boundary conditions, diaphragm layout, and cross-sectional geometry, on the first three modal frequencies. This process generated a comprehensive dataset, which then served as the basis for developing multivariate linear regression models. The resulting models yielded explicit predictive equations with excellent accuracy, with <i>R</i>² values exceeding 0.999 and root mean square error (RMSE) not greater than 0.31&#xa0;Hz. The principal contribution of this work lies in its hybrid methodology, which effectively combines physics-based FEM with data-driven regression modeling. This dual approach not only deepens mechanistic insight but also delivers practical utility. The derived closed-form expressions offer engineers an efficient preliminary design tool, significantly reducing the dependency on computationally intensive finite element simulations during early design phases.</p>