Current design codes for steel and steel-concrete composite structures are based on elastic, perfectly plastic material behaviour and can lead to overly conservative strength predictions due to the neglect of the beneficial influence of strain hardening, particularly in the case of stocky, bare steel cross-sections and composite beams under sagging bending moments. The Continuous Strength Method (CSM) is a deformation based design method that enables material strain hardening properties to be exploited, thus resulting in more accurate capacity predictions. In this paper, a strain hardening material model, which can closely represent the stress-strain response of hot-rolled steel, is introduced and incorporated into the CSM design framework. The CSM cross-section resistance functions, incorporating strain hardening, are derived for hot-rolled steel sections in compression and bending, as well as hot-rolled steel-concrete composite sections where their neutral axes lie within the concrete slab in bending. Comparisons of the capacity predictions with a range of experimental data from the literature and finite element data generated herein demonstrate the applicability and benefits of the proposed approach.