Abstract: Notched specimens are more and more widely used in fatigue studies. Since Neuber rule was proposed, the local stress-strain method has been used widely because of its simplicity. Conservative prediction results were usually obtained by this approach. The fatigue notch factor based on notched specimens has been used for the fatigue study instead of the stress concentration factor. However, the prediction precision has not been improved essentially. The stress gradient approach was proposed for the notched study with considerations of the stress gradient near the "hot point" and the concept of stress gradient was used in the stress field intensity approach. The dificult problem in the stress field intensity approach is how to decide the damage area accurately. The effective unification between the Neuber rule, the Peterson approach, and the stress field intensity approach can be achieved by the critical distance theory. The improvement of the finite element method supports the critical distance theory further. Now, better prediction results on high cycle fatigue were obtained by the critical distance theory, but this approach has not been much used for the predictions of low cycle fatigue.