The material modelling and design of hot-rolled and cold-formed structural steel cross-sections are addressed in this thesis. Regarding the material modelling, constitutive equations that accurately represent the stress-strain response of hot-rolled and cold-formed steels have been developed and calibrated based on a large dataset of coupon test results collected from the global literature. The models are suitable for use in advanced numerical simulations and parametric studies. For the design of structural steel elements, a deformation based design approach named the Continuous Strength Method (CSM), which provides an alternative treatment to the conventional concept of cross-section classification adopted in current design specifications and enables a rational exploitation of strain hardening, has been extended to cover both hot-rolled and cold-formed steels. The CSM design proposals were underpinned by existing test results collected from the literature in conjunction with additional cross-section tests on stocky hot-rolled I-sections conducted in the present study and numerical results obtained from validated finite element models. The design of cross-sections in compression, bending and combined loading has been addressed. The new design approach has been shown to yield a higher level of accuracy and consistency compared with the current codified design methods, and the reliability of the proposed design approach has been confirmed by performing statistical analyses. This study promotes the CSM as a universal design approach that now covers the design of stainless steel, aluminium alloy and structural carbon steel cross-sections. Recommendations for future developments to the CSM has also been made.