Global and local imperfections are required to capture accurate buckling loads and overall structural behaviour of axially loaded structural steel hollow sections in finite element (FE) models. In this paper, three methods of geometrical imperfections are considered for square and rectangular structural steel hollow sections: (i) creating the profile of the brace using a half sine wave, (ii) applying an equivalent notional lateral load at mid-length, and (iii) combining sinusoidal local imperfections with an equivalent notional lateral load for global imperfections. When modelling the initial shape of brace members with global imperfection at mid-length of the magnitude used to establish the European buckling curves (L/1000, where L is the length of the brace member), it was found that the equivalent notional lateral load methodology could best predict the buckling capacity of brace members when compared to physical test data and European buckling curves. However, both methodologies neglect the effect of local imperfection on the initial buckling loads. When it was included by generating a continuous sinusoidal wave along the member length, it did not affect the initial buckling loads, but gave a more overall representative behaviour of the brace members.The FE model is then validated using sixteen cyclic tests for brace members. The FE results are found to match the physical tests values relatively well. In other words, when comparing the ratio of yield force, buckling resistance, and total energy dissipated estimated from the FE model to the measured values in physical tests, the mean values are found to be 1.04, 0.99 and 1.24, respectively, with a coefficient of variation of 0.07, 0.07 and 0.17, respectively. (C) 2017 Elsevier Ltd. All rights reserved.