Circular hollow sections (CHS) are widely used in a range of structural engineering applications. Their design is covered by all major design codes, which currently use elastic, perfectly-plastic material models and cross-section classification to determine cross-secti\on compressive and flexural resistances. Experimental data for stocky sections show that this can result in overly conservative estimates of cross-section capacity. The continuous strength method (CSM) has been developed to reflect better the observed behaviour of structural sections of different metallic materials. The method is deformation based and allows for the rational exploitation of strain hardening. In this paper, the CSM is extended to cover the design of non-slender and slender structural steel, stainless steel and aluminium CHS, underpinned by and validated against 342 stub column and bending test results. Comparisons with the test results show that, overall, the CSM on average offers more accurate and less scattered predictions of axial and flexural capacities than existing design methods.