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This study introduces a novel approximate model (AM) aimed at optimizing the design of cross-beam multi-axis force/moment sensor. It considers the characteristics of flexure hinges in elastic beams and the flexibility of beam joints, resulting in improved accuracy and broader solutions for equivalent stresses and natural frequencies compared to existing approximate models in the literature. Model validation is carried out by comparing the results with the finite element model in different cases that each case contains 1000 simulations. Validation cases combine different sensor dimensions with different forces, moments, material properties, and center hub shapes. Each validation case typically requires approximately 19 h using the finite element method (FEM) and just 1 sec with the AM. Furthermore, by using the Gaussian process and partial dependence plots, the sensitivity of the model accuracy on normalized sensor dimensions is investigated. The evaluation of model linearity and dimension normalization allows for the utilization of the novel approximate model beyond the provided dimension range, while still adhering to the normalized parameters. The implementation of AM in the design optimization problem demonstrates its suitability and advantages compared to existing literature and FEM results. When compared to finite element solutions within the sensor workspace, the approximate model exhibits a stiffness error of 5%, a strain error of 2%, a fundamental frequency error of 3%, and an equivalent stress error of 8%, while maintaining correlations of axial sensor properties above 98%. [ABSTRACT FROM AUTHOR]