This paper presents a combined study of theoretical solutions and experimental tests on the deformation processes of non-contact, point contact, line contact and secondary buckling of the sleeved column. In this study, a mechanical model based on the second order equilibrium differential equations with small deflection is developed, and two types of sleeved column are fabricated and tested using six specimens. And in the tests, it is observed that the ultimate axial load capacity and ductility of the sleeved column are substantially increased, and the axial load capacity will be reduced due to the small slenderness ratio of the inner core, large stiffness of the sleeved column and the large gap between the inner core and the sleeve. Furthermore, the study investigates the effects of the stiffness ratio of the inner core to the sleeve on the column's buckling mode transition process. Finally, a discussion on the comparison between the analytical results by the proposed mechanical model and the tested results is also presented.