ln this paper. the relation between the maximum strain at the notch root and the J integra, value has been derired for a notch wfth a semi. elliptical end. It is proposed that the maximum strain energy density or the maximum strain criterion controls the cracking at the notch roots. The relation indicates that notch J. integra, fracture toughness depends not only on the material and the magnitude of the notch root radius of curvature(or notch width 1 but also upon the magnitude of ellipticity. In the same Why. the relation derived in this paper shows that, when the strain concentration at notch root is predicted by the value ofthe 3-integral. the effect ofellipticity should not be neglected, in addition to the direct effect of the magnitude of notch root radius of curvature.