A comprehensive experimental investigation into the axial compressive response of concrete-filled double skin tubular (CFDST) sections with stainless steel square and rectangular outer tubes is presented. A total of 28 tests was carried out. The experimental setup and procedures are described, and the test observations are fully reported. The test results are employed to assess the applicability of the current European and North American design provisions for composite carbon steel members to the design of the studied CFDST cross-sections. Modifications to the current design codes are also considered—a higher buckling coefficient k of 10.67 to consider the beneficial restraining effect of the concrete on the local buckling of the stainless steel outer tubes and a reduction factor η to account for the effective compressive strength of high strength concrete. Overall, the comparisons revealed that the existing design rules may generally be safely applied to the prediction of the compressive resistance of CFDST cross-sections with stainless steel outer tubes, while the modified design rules offered greater accuracy and consistency.