This chapter introduces a computational framework utilizing Variable Order Secant Matrices (VOSM) for the nonlinear geometric analysis of thin-walled open sections. Thin-walled members, known for their high strength-to-weight ratios, are crucial in structural engineering but present challenges due to their complex flexural–torsional coupling behavior under large deformations. Using shell theory, a 3D beam finite element with 14 degrees of freedom is formulated to capture axial, flexural, shear, and torsional deformations. The strain energy of these elements is expanded through the Taylor series to develop higher-order secant stiffness matrices, enhancing accuracy in the large deformation analysis. The VOSM approach is validated through classical examples of pre and postbuckling behaviors under axial loads and end moments, demonstrating both accuracy and computational efficiency. This method proves highly effective for modeling the nonlinear behavior of slender, thin-walled sections subjected to combined torsional and flexural loads.