The applicability of the CED, that has the meaning of strain energy area density without any restriction on constitutive equation, to the resistance evaluation of fiber pulling out in fiber reinforced composites was studied, for an axisymmetric model with a cylindrical crack between a fiber and matrix, by using the discontinuous model. The path-independent expression of CED with no restriction on constitutive equation was derived first and the finite element analyses of the model were carried out to investigate the properties of CED for fiber debonding problem. The CED was evaluated not only by the derived path-independent expression but also by other methods and it was demonstrated that the evaluation of CED can be conducted easily taking the effects of friction in debonded interface and singularity at the edge of debonding, that are difficult to evaluate when the conventional methods are employed, into consideration.