This paper presents analytical studies on the long-term behaviour of circular concrete filled steel tubular (CFT) columns under central axial loading. Two loading cases are considered in this study: (1) a load applied only at the inner core concrete of a CFT column; and (2) a load applied simultaneously on both the inner concrete and the steel tube. Analysis methods are formulated based on compatibility, equilibrium conditions, and a number of assumptions for the two loading cases. Bond behaviour between the inner concrete and the steel tube along with confinement created by the steel casing are considered in the formulation. Experiments were performed for CFT column specimens under the aforementioned two loading cases to verify analysis methods. Analysis results exhibit good agreement with test results, and therefore the validity of the assumptions used in the formulation and the accuracy of analysis methods is proven. Furthermore, the following features of the long-term behaviour of circular CFT columns under these loading cases are revealed by test and analysis results. In the case of loading at the inner concrete of the CFT column, the strains of both the concrete and steel tube are non-linearly distributed along the longitudinal axis of the CFT column because of the bond stress and the confinement effect. Slip occurs and becomes larger with time due to the difference between the strain distributions of the concrete and the steel tube, which also increases with time. In the case of loading on the entire section of the CFT column, the strains of both the concrete and steel tube are uniformly distributed along the longitudinal axis of the column. As loading time increases, however the stress acting on the concrete section decreases, while the stress of the steel tube section increases. The confinement effect of the concrete does not appear at initial loading or in long-term deformation.