Proper material constitutive models for concrete-filled tube (CFT) columns of circular cross section and subjected to pure bending moment are proposed. These material models are implemented into the Abaqus finite element program and verified against experimental data. It has been shown that the steel tube does not provide good confining effect to the concrete core when the CFT columns is subjected to pure bending moment. When the diameter-to-thickness ratio of the CFT columns is small, the behavior of the CFT column is the same as the steel tube without a concrete core.