Cold-formed steels are generally characterized by a rounded stress-strain response with no sharply defined yield point. It is shown herein that this material behaviour can be accurately described by a two-stage Ramberg-Osgood model provided that the values of the key input parameters can be established. The focus of the present paper is to develop predictive expressions for these key parameters to enable the full engineering stress-strain response of cold-formed steels to be represented. The predictive expressions are based on the analysis of a comprehensive set of material stress-strain data collected from the literature. In total, more than 700 experimentally-derived stress-strain curves on cold-formed steel material have been collected from around the world, covering a range of steel grades, thicknesses and cross-section types. The strength enhancement in the corner regions of cold-formed sections has also been analysed and the applicability of existing predictive models has been evaluated. Finally, standardized values of strain-hardening exponents used in the Ramberg-Osgood model have been recommended for both flat and corner material in cold-formed steel sections. The proposed stress-strain curves are suitable for use in advanced numerical simulations and parametric studies on cold-formed steel elements.