Abstract: A mechanical model of the interfacial transcrystallinity in the composite of polyetheretherketone (PEEK) reinforced with carbon fiber was obtamed on the basis of its structural ch arateristic.Young's modulus of the transcrystallinity in the direction perpendicular to the fibre ov which it grows was found to be greater than that of the bulk opherulite,and depend on the lamellar structure in the transcrystallinity.It incre ases with the increasing of lamellzr length or thickness,but decrease;with the increasing of the lamellar width.The reason was discussed,and the result was verified with experiments.