The contribution to the critical shear stress of nanocomposites caused by the interaction between screw dislocations and core-shell nanowires (coated nanowires) with interface stresses was derived by means of the MOTT and NABARRO’s model. The influence of interface stresses on the critical shear stress was examined. The result indicates that, if the volume fraction of the core-shell nanowires keeps a constant, an optimal critical shear stress may be obtained when the radius of the nanowire with interface stresses reaches a critical value, which differs from the classical solution without considering the interface stresses under the same extal conditions. In addition, the material may be strengthened by the soft nanowires when the interface stresses are considered. There also exist critical values of the elastic modulus and the thickness of surface coating to alter the strengthening effect produced by it.