A buckling loads formula based on Generalised Beam Theory (GBT) was proposed, which could be used in non-linear elastic metallic materials thin-walled compressed members, such as stainless steel. By introducing non-linear stress-strain relations and instantaneous elastic modulus, the modifications were incorporated in the conventional GBT, and the expressions were formulated to calculate buckling loads of stainless steel members buckling in local, distortional and global modes. Compared with the existed test results, it is shown that linear elastic method cannot deal with stainless steel, while the results of proposed method are much more reliable. Moreover, the modified GBT method with deformation plasticity theories produces safer results, which could be used in determining buckling loads of non-linear metallic materials thin-walled members in compression, as well as structural design and further researches.