The aim of this paper is to develop a robust numerical model for cold-formed steel square and rectangular structural hollow sections for use as axial loaded members in earthquake engineering applications. Pseudo-static cyclic physical tests of cold-formed steel brace specimens using axially loading are used to develop and calibrate a robust numerical model that mimics the results from the tests. A nonlinear fibre based beam-column element model which considers the spread of plasticity along the element is used. This numerical model includes a low cyclic fatigue model, which wraps the nonlinear fibre based beam-column element material in order to capture fracture in the braces. New parameters to be used for the fatigue model are introduced in this paper. Comparisons of the maximum tensile force (Fmax), initial buckling load (Fc), number of cycles to fracture, the total energy dissipated (Wtot) and the energy dissipated at the first cycle of ductility of 4 (Wl=4) between the numerical models and the physical tests are carried out. In general, the models captured the salient response parameters observed in the physical tests. It is found that the numerical model gives a good prediction of the maximum measured tensile force (Fmax) and initial buckling load (Fc) with the mean values being 0.93 and 0.95 of those measured in the physical tests, respectively. The corresponding coefficients of variation (CV) are 0.11 and 0.08, respectively. Moreover, the mean values of the total energy dissipated (Wtot) and the energy dissipated at the first cycle of ductility of 4 (Wl=4) for the numerical model are found to be 1.12 and 0.98, of those measured in the physical tests, respectively. The corresponding coefficients of variation (CV) are 0.13 and 0.20, respectively. Furthermore, the numerical model was validated using another set of independent physical tests. This validated brace element model can be used in future numerical models of concentrically brace frames buildings to predict the performance of the complete structures under earthquake loading.