Abstract: Fracture of bi-materials often occurs at or near the interface, but the mechanism and criterion of interface fracture are not clearly known yet. A simulation method of molecular dynamics is introduced to simulate the interface crack initiation, from which the correlations between the interface stress and the interface fracture are acquired. Though a quite simplified simulation model is used in simulation of molecular dynamics, the result also reveals some intrinsic features that are useful to understand the process of bi-material interface fracture. By laying out an initial crack near the interface, stress concentration is caused at the interface and the interface crack initiation happens. From the simulation results of molecular dynamics, a bi-material interface crack initiation criterion viz. an interface fracture criterion is proposed.