In order to investigate the fracture process of CFRP with high toughness, a plate specimen of a uni-directionally reinforced AS4/PEEK is subjected to transverse tension at room temperature. The results obtained are summarized as follows; (1) At 83% of fracture stress, small cracks are initiated along the interfaces of fiber and matrix in a group on or near the edge of specimen. (2) The cracks are semi-circular and they are arrested just after the initiation. (3) Although the number of the cracking regions increases as the applied stress increases, the area of each cracking region does not grow due to the crack arrest. (4) The boundary element analysis and the finite element analysis reveal that the arrest is caused by the cylindrical shape of the interface. (5) The cracks restart to grow and make coalescence when the stress field near the crack tip satisfies the condition of crack kinking. (6) The main crack formed brings about the specimen breaks down when the stress intensity factor reaches the macroscopic toughness, which is evaluated by DCB specimen.