Abstract: The asymptotic displacement fields for interfacial cracks between two dissimilar materials were used to construct enrichment functions for elements around crack tips in the extended finite element methods (XFEM). The discretization scheme in XFEM does not need to be aligned with material interfaces. Three types of enrichment functions: enrichment functions for weak discontinuities, heaviside enrichment functions and crack tip enrichment functions, are applied to formulate XFEM approximation. Subsequently, the interaction integral methods are derived for computing stress intensity factors (SIFs) of interfacial cracks between two dissimilar materials. Results show that the XFEM can accurately evaluate SIFs of interfacial cracks without the need of conforming meshes with material interfaces.