This paper presented the theoretical solutions and the experimental tests of the deformation processes of the inner core constrained by flexible sleeve in a sleeved column, and proposed the design formulas, relevant details and the nonlinear computation model of inner core's axial load-displacement. The results indicate: (1) when the stiffness ratio between the inner core and the sleeve is smaller than 0.005, the inner core will snap from low order mode to high order mode; when the stiffness ratio is larger than 0.005, the inner core and the sleeve will buckle together laterally; (2) the stiff sleeve, small slenderness ratio of the inner core and the large net clearance between the inner core and the sleeve exert adverse effects on the remarkable improvement of the inner core's bearing capacity; the parts of the inner core outside the sleeve are most vulnerable, their length must be small and the parts must be strengthened to avoid the local buckling of the inner core; and (3) compared with the conventional circular steel tube, the compression capacity of the inner core has been improved substantially and its ductility has also been greatly improved.