The fracture behavior of brittle materials under biaxial plane stress has been investigated by means of numerical simulation method with software MFPA2D (Material Failure Process Analysis). The aims of this study are to clarify the fracture dependence of brittle material on biaxial plane stress state. The observation of crack initiation and fracture behavior reveals that the biaxial stresses have strong influence on the fracture properties of glass. Thus, the fracture criterion by the stress intensity factor was questioned for the biaxial plane stress issues. It is confirmed that the tensile stress parallel to the crack plane is an important factor affecting crack arrest, while the compressive stress parallel to the crack plane contributes to crack opening.