The use of advanced analytical and numerical modelling in structural engineering has increased rapidly in recent years. A key feature of these models is an accurate description of the material stress-strain behaviour. Development of standardised constitutive equations for the full engineering stress-strain response of hot-rolled carbon steels is the subject of the present paper. The proposed models, which offer different options for the representation of the strain hardening region, feature an elastic response up to the yield point, followed by a yield plateau and strain hardening up to the ultimate tensile stress. The Young's modulus E, the yield stress fy and the ultimate stress fu are generally readily available to the engineer, but other key parameters, including the strains at the onset of strain hardening and at the ultimate stress, are not, and hence require predictive expressions. These expressions have been developed herein and calibrated against material stress-strain data collected from the literature. Unlike the widely used ECCS model, which has a constant strain hardening slope, the proposed models, reflecting the collected test data, have a yield plateau length and strain hardening characteristics which vary with the ratio of yield to ultimate stress (i.e. with material grade). The proposed models require three basic input parameters (E, fy and fu), are simple to implement in analytical or numerical models, and are shown herein to be more accurate than the widely employed ECCS model. The proposed models are based on and hence representative of modern hot-rolled steels from around the world.