An accurate stress-strain relationship is needed for use in the advanced numerical modelling of cold-formed light-gauge steel members covering a wide range of strains. Existing stress-strain models for carbon steels are either capable of accurate predictions over a limited strain range or defined using many material parameters for a full range of strains. The values of some material parameters are not always available in existing design codes. This paper presents two stress-strain models for light-gauge carbon steels, which are capable of accurate predictions over the full range of tensile strains up to the strain at the ultimate stress. Both stress-strain models are solely defined using either three basic Ramberg-Osgood parameters (E0, σ0.2, and n) or even two basic parameters (E0, and σ0.2), and are based on a careful interpretation of existing experimental data of virgin materials and materials from flat portions of cold-formed steel sections. The accuracy of these two proposed models is demonstrated by comparing their predictions with experimental stress-strain curves.