Abstract: In this paper, we prove the independence of the path of the imegrals near model i II track tips in the plate of the orthotropic composite material.Then we derive the computing formulae of the J-integrals at the cases of and by using a complex variable method and redueing J-imegrals to compley farmThe J-integral computational formulae derived this paper have certain reference value for the theoretical researches and the experimental verifications in the plane fracture for composite material.