Abstract: In this paper, we discuss J-integrals near models I and II crack tips for the plates of linear-elastic isotropic homogeneous material and orthotropic composite material, using the theories of complex function and calculus, and obtain the result as follows:(1) The various J-integrals are transformed into standard form of line integrals with respect to coordinates: J=∫_rp(x,y)dx+Q(x,y)dy (2) Independence of path of the various J-integrals is proved.(3) Computing formulae of J-integrals are derived.