Rolling back-up rolls require high fracture toughness, particularly in the shaft portion, and high-hardness in the sleeve portion. The rolls are classified into two types; one is an integrated type and the other is a shrink-fitted type consisting of a sleeve and a shaft. The shrink-fitted roll has several advantages, for example, suitable materials can be chosen and the shaft can be reused by replacing the damaged sleeve. However, during use if the residual permanent deflection occurs, the roll cannot be used anymore. In this paper, an elastic-contact finite element method FEM analysis is performed to explain the residual permanent deflection mechanism. It is found that the quasi-equilibrium stress zone with the residual displacement causes the permanent slippage in the axial direction. In a similar way, the interface creep in the circumferential direction can be also explained from the quasi-equilibrium stress zone with the residual displacement.