Abstract The finite element displacement method considering both geometrical nonlinearity and material non-linearity has been used to investigate the post-buckling behaviour and the ultimate strength of thin-walled nonplanar (three-dimensional) structural members. The two types of nonlinearities are based on Lagrangian coordinates and the flow theory of plasticity, and the formulations are developed using the variational principle and the incremental variational principle. The tangent stiffness matrix which is derived explicitly up to a point prior to volume integration, has been found to be quite efficient. The cases of a hat-section beam under a concentrated load for a web crippling study and a channel section subjected to combined bending and torsion are used to show the capabilities of the computer program. Results indicate that the conventional linear, elastic analysis over-estimates the strength of thin-walled members and may not even be a useful approximation and that the structure may be excessively deformed when approaching the ultimate load. The study also demonstrates the merit of using the finite element method for detailed investigations of particular problems.