This paper presents modelling approaches for the global and distortional buckling of cold-formed built-up steel sections using the finite element software packages, ANSYS and ABAQUS. Thin thickness of the cold-formed steel causes nonlinear behaviour due to local and distortional buckling, thus careful consideration is required in modelling for numerical analysis. Implicit static modelling using ANSYS provides unstable numerical results as the load approaches the limit point but explicit dyamic modelling with ABAQUS is able to display the behaviour even in post-buckling range. Meanwhile, axial load capacities obtained from the numerical analysis show higher values than the experimental axial capacities, due to eccentricity during the test. Axial capacities of the cold-formed steel obtained through numerical analysis requires reduction factor, and this paper suggests 0.88 for the factor.