Purpose – Although the actual residual stress distribution in any structural steel member can be only obtained by experimental measurements, it is known to be a difficult, tedious and inefficient piece of work with limited accuracy. Thus, besides aiming at clarifying structural designers and researchers about the possible ways of modelling residual stresses when performing finite element analysis (FEA), the purpose of this paper is to provide an effective literature review of the longitudinal membrane residual stress analytical expressions for carbon steel non-heavy sections, covering a vast range of structural shapes (plates, I, H, L, T, cruciform, SHS, RHS and LSB) and fabrication processes (hot-rolling, welding and cold-forming). Design/methodology/approach – This is a literature review. Findings – Those residual stresses are those often required as input of numerical analyses, since the other types are approximately accounted for through the s-e curves of coupons cut from member walls. Practical implications – One of the most challenging aspects in FEA aimed to simulate the real behaviour of steel members, is the modelling of residual stresses. Originality/value – Besides aiming at clarifying structural designers and researchers about the possible ways of modelling residual stresses when performing FEA, this paper also provides an effective literature review of the longitudinal membrane residual stress analytical expressions for carbon steel non-heavy sections, covering a vast range of structural shapes (plates, I, H, L, T, cruciform, SHS, RHS and LSB) and fabrication processes (hot-rolling, welding and cold-forming).