The threshold repeated stress (nominal) to develop crack at the root of a notch is different from the threshold one (nominal) to spread the developed crack. At the branch point these two kinds of threshold stresses become equal to each other. In steel, branch point has close relation with the yield point of the material. In this paper it is shown that, although annealed copper shows no definite yield point in tension, branch point can be observed in rotary bending test of notched copper specimens. At the branch point the fatigue limit expressed by the maximum stress at the root of notch is equal to the stress at which tangent modulus of fatigued material begins to decrease sharply. It is suggested that severely deformed zone at the root of notch, appeared before fatigue crack is formed there, plays an important role in the mechanism of fatigue crack propagation.