Nanocomposites have shown excellent mechanical and physical properties; however, their properties are seriously affected by the nucleation of misfit defects at the interfaces between the inclusion and the matrix. Based on the energy rule, the nucleation criteria for a misfit extended dislocation dipole (MEDD) and a misfit screw dislocation dipole (MSDD) are analytically given. Furthermore, we systematically investigate the effects of the geometrical and mechanical factors, such as the radius of the inclusion, the misfit strain, the shear modulus ratio and the stacking fault energy, on the competitive nucleation between MEDD and MSDD. It is found that the stacking fault energy has a decisive effect on the competitive nucleation of MEDD and MSDD. The critical stacking fault energy for the nucleation transferring from MSDD to MEDD increases with the increase of the shear modulus ratio and decrease of the misfit strain, while it is almost not affected by the inclusion radius.