This paper presents a computational model for determining the axial responses of short circular steel–reinforced concrete-filled steel tubular (SRCFST) columns. A novel confinement model is formulated for the concrete core, which is effectively confined by the external circular steel tube and the embedded steel section. The modelling scheme of the confinement is programmed using a mathematical model that utilises fibre-element discretisation of column cross-sections. The numerical predictions are verified by experimental measurements and results obtained from finite-element analysis, demonstrating the accuracy of the modelling technology. In addition, existing concrete confinement models for concrete in circular concrete-filled steel tubular columns are assessed. The new confinement model is shown to be superior in replicating the responses of SRCFST columns. The influences of the design parameters on the column’s performance are numerically investigated and ranked in order of importance through a sensitivity analysis. In this study, not only is the validity of current design standards in determining the axial load capacity of SRCFST columns examined but a new design formula is also proposed. The proposed confinement model can be employed in numerical procedures for the inelastic simulation of SRCFST columns; the design formula is suitable for use in practical design.