The construction of lightweight structures poses new design challenges as a result of the different mechanics of deformation experienced by thinner-plated structures. Because of a reduced bending stiffness, thin plates are particularly sensitive to welding-induced distortions, which include a curvature, in addition to the axial and global angular misalignment observed on thick plates. The curvature shape and amplitude determine a local angular misalignment at the welded joint, which causes non-negligible secondary bending effects. Therefore, the commonly used stress magnification factors k m solution for flat plates need a further development to include the curvature effect. This study proposes new analytical formulations, which extend the applicability of the existing solutions to the assessment of the structural stress of a curved thin plate under an axial load. The improved formulations are consistent with the geometrical non-linear finite element analysis under compression (up to ∼ 80% of the buckling limit) and tension (up to the yield strength). A sensitivity analysis is presented in order to show the dominant role of the curvature effect in the estimation of the k m factor. Regardless of the load applied, the presence of the curvature causes a flat plate solution inaccuracy greater than 10% when the local angular misalignment is more than 1.25 times higher than the global angular misalignment in the case of a thin and slender structure.