Abstract: A buckling model of the line-contact segment between the axially compressed inner core and the flexible sleeve in a sleeved column is proposed and the deformation process of the inner core after the line contact between the inner core and the sleeve is studied. Expressions of the deflection, moment, shear and contact forces of the inner core after the buckling of the line-contact segment are derived according to the second order differential equilibrium equations for small deflection. The following rules can be obtained through the numerical examples: (1) If the ratio of the inner-core stiffness to the sleeve stiffness is small enough, buckling of line-contact segment takes place after the inner core undergoes sequential deformations characterized by a single point contact and a line contact with the sleeve, and eventually the inner core undergoes deformation characterized by two points contact with the sleeve having a buckled segment between them; (2) If the ratio of the inner-core stiffness to the sleeve stiffness is large enough, the inner core fails together with the sleeve during the line-contact phase as a result of large deflection without buckling of line-contact segment. This proposed model can also be applied to simulate the buckling of the line-contact segment between the inner core and the rigid sleeve.