Abstract: This paper introduces an extended Voronoi cell finite element model (X-VCFEM) proposed by Ghosh for modeling the propagation of interfacial debonding and matrix cracking in fiber reinforced composite materials. A series of criteria based on the theory of interface and fracture mechanics were proposed for assessing the damage development，which includes the interfacial debonding，the direction of damage at the interface and the crack propagation in the matrix. With a re-mesh strategy，comparisons of X-VEFEM simulations of one Voronoi element with reference results of traditional finite element method validate the effectiveness of X-VCFEM model .Meanwhile，the initiation and propagation of interfacial debonding and matrix cracking in fiber reinforced composite materials of random distributed fibers were simulated. The results show that this model for modeling the initiation and propagation of interfacial debonding and matrix cracking in complex fiber reinforced composite materials has the advantages of fast speed and high precision.