Through the development of an innovative full cross-section tensile testing method, a programme of experiments was conducted to investigate the influence of average cross-section properties on the constitutive relationships for carbon steel, to validate the use of an elastic linear hardening model in practical design, and to assess the resulting accuracy enhancements to the new deformation-based continuous strength method (CSM) of structural steel design. A total of seventeen full cross-section tensile tests on hot-rolled I-sections, hollow sections and cold-formed hollow sections were performed and these were compared with coupon test data obtained from a supplementary programme of 14 tensile coupon tests and data carefully obtained from the literature. The overall behavioural response of the cross-section tensile tests demonstrated that assuming an elastic, linear hardening material model for the CSM is a reasonable assumption and the previous assumption concerning the magnitude of the strain-hardening modulus, based upon the recommendations of EN 1993-1-5, is overly conservative. A revised suite of material models was presented and was shown to furnish the CSM capacity equations with a higher degree of accuracy when compared against experimental data.