The structural performance of circular concrete-filled double skin tubular (CFDST) cross-sections with stainless steel outer tubes has been examined herein based on experiments and numerical modelling. A laboratory testing programme comprising a total of 22 four-point bending tests was performed on seven CFDST cross-sections with varying concrete grades. The details of the test rig and procedures, as well as the key test observations, including the failure moment capacities, moment–curvature curves and failure modes, are fully reported. A numerical modelling programme was then carried out; a finite element (FE) model was first established to replicate the test observations, and then adopted to conduct a parametric study to acquire further FE data over a broader spectrum of material strengths and cross-section slendernesses. Based on the combined set of test and FE results, the general design provisions for concrete-filled carbon steel members in the current European and American design codes were evaluated for their applicability to the studied CFDST cross-sections. Overall, the results revealed that both of the examined design codes yield unduly conservative (less so for the higher concrete grades) and scattered moment resistance predictions, though some moment resistances predicted from the European code were on the unsafe side. Modifications, including a concrete reduction factor η to reflect the reduced relative effectiveness of using higher concrete grades and a modified stress distribution considering the partial spread of plasticity, were proposed and shown to improve the consistency of the resistance predictions. Finally, the reliability of the current and modified design rules was demonstrated through statistical analyses.