Abstract: The crack embedded in fibers is crucial in the fracture of fibers of the composite material.The boundary element method for multiple media axisymmetrical problems is used in this paper to calculate the stress intensity factor for a penny shape crack embedded in a fiber of the composite material.The influences of the modulus ratio of the matrix to fiber,the volume ratio and poisson's ratio on the stress intensity factor are also analyzed.The results are useful in the analysis of the mechanism of composites failure in the form of fiber fracture.