[Objective] This study aims to establish an efficient and reliable mechanical model to accurately evaluate internal forces and stresses within the force transmission system of fully balanced rack-and-pinion vertical shiplifts, providing reliable theoretical foundations for engineering design, structural optimization, and safety assessment. [Methods] Based on a comprehensive analysis of the structural configuration, material properties, and loading conditions of the nut-column force transmission system, a novel semi-infinite double elastic coupling foundation beam model is proposed. In this approach, the nut column and adjustment beam were modeled as interacting elastic bodies while incorporating their mutual deformation and force transmission mechanisms. To describe axial load transmission at the interface with complex contact mechanics, exponential distribution functions were introduced. The model integrated elastic foundation beam theory with fundamental mechanics of materials, enabling the derivation of closed-form expressions for deflection, internal forces (bending moments and shear forces), and stresses (normal and shear) in both the nut column and adjustment beam. These expressions accurately characterized the distinct mechanical behavior of the force transmission system under different loading scenarios. [Results] Theoretical predictions were validated through physical model testing, yielding several key findings. (1) Model validation: At x=L=4 950 mm, both deflections and internal forces of the nut column and adjustment beam approached zero, demonstrating the validity of the semi-infinite beam assumption. This simplified boundary condition treatment and provided a novel analytical approach for similar structural systems. (2) Parameter sensitivity insights: By comparing results under two interface constraint assumptions with α=π and α=2π, the model revealed the significant impact of α on structural response. While the α=2π assumption yielded more conservative results, α=π aligned better with experimental data. (3) New understanding of stress distribution: Contrary to conventional assumptions, the maximum bending moment in the nut column occurred not at the end but near it, indicating that the traditional use of end-moment M0 as the design load was inadequate. Moreover, except for axial force, all other internal forces in the adjustment beam exceeded those in the nut column, providing critical insights for structural optimization. (4) Stress comparison: Calculated stress values, though slightly exceeding experimental results, remained within allowable stress limits, demonstrating the rationality of the current design. The results obtained with α=π exhibited better agreement with experimental data, further confirming the model’s reliability. [Conclusion] The nut column force transmission system of the Three Gorges Ship Lift is structurally robust. The proposed semi-infinite elastic foundation beam model proves effective and applicable for similar designs. Incorporating the Pasternak elastic foundation beam model in future studies can further enhance analytical accuracy, providing a promising direction for both theoretical advancements and engineering applications.