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In the present paper the J-integral for an elliptical notch has been analytically calculated by using the stress distribution for the case of an isolated ellipse under remote tensile loading. The material is thought of as obeying a purely linear elastic law and the difference between the J-integral of a crack and the equivalent ellipse is discussed. For instance it is analytically verified that when the notch tip radius tends toward zero the well known J-integral formula for a crack is obtained. Finally, as an engineering application, an accurate formula is given for the evaluation of the Notch Stress Intensity Factors of a crack from the peak stress of an equivalent ellipse.