In recent years, composite columns have gained much attention in offshore and marine engineering. This paper, with the motivation of a better design for circular straight double skin steel tubes confined concrete (DSSTCC) columns, theoretically explores the local buckling of the internally stiffened inner skin in this column. Firstly, the force analysis of a DSSTCC stub column was conducted, and its common failure modes were outlined. Based on the similar structural performance of the inner tube and the fixed circular arch, a concise buckling analysis model was built up. Then different buckling modes of clamped circular arches under the uniform radial load were presented. The ultimate load-carrying capacity of internally stiffened inner tubes under different buckling modes was also discussed, which shows relatively high dependence on the structural stability. Next, the calculation method of the expected ultimate hoop compressive stress was given, and the main computational procedure of the cross-sectional slenderness limit for internally stiffened inner skins was illustrated. In addition, a very simple prescriptive equation that considers the elastic modulus, the yield stress, and the formed arch's central angle value was fitted to estimate the cross-sectional slenderness limit for inner tubes with internal stiffeners, with which a slender cross-section can be delineated from an effective one. Meanwhile, the elastic buckling stress of the inner tube was also given. Finally, the applicability of the proposed methodology to materials with the bilinear model, the bilinear plus nonlinear hardening model, the idealized multilinear model, or the Ramberg-Osgood model was investigated, thereby demonstrating its good adaptability to these four common nonlinear constitutive models.