The light weight and high strength-to-mass ratio of thin-walled boxed sections have incited interest in their widespread use in the construction of domes. However, the installation of these sections in forming the dome geometry has induced initial twists and curving features, to which their mechanical response has rarely been explored. Therefore, the structural performance of a structure with thin-walled twisted box sections is numerically studied in this paper, employing ANSYS, the verification of which is carried out through a comparison with experimental results. Additional components examined include the longitudinal stiffening rib, diaphragm, and web. The effects of variations in the thicknesses of these member plates on the mechanical behaviors are investigated. In general, the ultimate capacity of the structure is improved by increasing the thickness of the longitudinal stiffening rib, diaphragm, and web, but the strengthening effect of the stiffener is limited by a certain thickness enhancement. The common failure mode of the initial model is found to be an overall elastic-plastic buckling. A reduction in the thickness of the stiffener or web creates a curving deformation zone in the lower arch at the ultimate capacity, whereas the diaphragm thickness has little effect on the failure mode of the model.