The experiments indicate that stainless steels in tension deform plastically more than stainless steels in compression. Therefore, the strain hardening of stainless steels in compression is much faster than that of stainless steels in tension. The full-range two-stage constitutive model for stainless steels assumes that stainless steels follow the same stress-strain behavior in compression and tension, which may underestimate the compressive strength of stainless steel tubes. This paper presents a fiber element model incorporating the recently developed full-range three-stage stress-strain relationships based on experimentally observed behavior for stainless steels for the nonlinear analysis of circular concrete-filled stainless steel tubular (CFSST) short columns under axial compression. The fiber element model accounts for the concrete confinement effects provided by the stainless steel tubes. Comparisons of computer solutions with experimental results published in the literature are made to examine the accuracy of the fiber element model and material constitutive model for stainless steels. Parametric studies are conducted to study the effects of various parameters on the behavior ofcircular CFSST short columns. A design model based on Liang and Fragomeni's design formula is proposed for circular CFSST short columns and validated against results obtained by experiments, fiber element analyses, ACI-318 codes and Eurocode 4. The fiber element model incorporating the three-stage stress-strain relationships for stainless steels is shown to simulate well the axial load-strain behavior of circular CFSST short columns. The proposed design model gives good predictions of the experimental and numerical ultimate axial loads of CFSST columns. It appears that ACI-318 codes and Eurocode 4 significantly underestimate the ultimate axial strengths of CFSST short columns.