Abstract: A mechanical model of line contact between the inner core and the sleeve with finite stiffness in a sleeved compression member under axial compression is proposed. The formulae for deflection, moment, shear and contact reaction of the inner core during point contact and line contact between the inner core and the sleeve are derived according to the second order equilibrium differential equations of small deflection. The formulae and application examples indicate that the proposed formulae satisfy essential continuity and compatibility conditions at the transition from point contact to line contact between the inner core and the sleeve. The proposed model can also be applied to simulate the line contact between the inner core and the rigid sleeve.