Abstract: The deformation processes of the non-contact, point-contact, line-contact, post-buckling of line-contact, etc., between the flexible sleeve and the axially compressed inner core with initial deflections in a sleeved column, are researched theoretically. Expressions of the deflection, moment, shear and contact reaction of the inner core and the sleeve are derived, adopting the second order differential equilibrium equations of a small deflection. Two types of sleeved columns are experimentally studied. The following results can be obtained: 1) If the stiffness ratio between the inner core and the sleeve is smaller than 0.005, the inner core snaps from the low order mode to the higher order mode; if the stiffness ratio is larger than 0.005, the inner core fails together with the sleeve due to lateral buckling; 2) Stiff sleeve, small slenderness ratio of the inner core and large net clearance between the inner core and the sleeve exert adverse effects on the remarkable improvement of inner core's bearing capacity. The parts of the inner core outside the sleeve are the most vulnerable; their lengths must be small and the parts must be strengthened to avoid the local buckling of the inner core.