A fragmentation test has been developed for the study of the influence of the adhesive characteristics of the interface between reinforcing fibers and the matrix on the development of matrix cracking at a cracked single fiber location. The present paper examines the numerical modeling of the crack extension process within the matrix region. The numerical modeling focuses on the application of boundary element techniques to the study of an axisymmetric fiber-matrix model and quasi-static crack extension criteria are employed to determine the path of crack extension. The result for the crack extension patterns obtained from the numerical models are compared with the results derived from the experiments. It is shown that elastic fracture mechanics simulations of quasi-static crack extension can successfully model the observed experimental phenomena.