In this paper, the debonding initiation and propagation in the bundled fibers-matrix composite is studied by utilizing a finite element method, which incorporates the bilinear cohesize zone model. The cohesive zone model parameters are adjusted so that the mechanical response of the model fits to that obtained in an experiment. Furthermore, the model performance is verified against three additional experimental datasets. The study reveals that for this particular specimen and loading condition, the interface debonding stably propagates until the applied load reaches its maximum. After the maximum applied load, the debonding propagates rapidly, and finally, the bundled fibers breaks completely.