Abstract: According to the characteristic that fatigue damage is partial, on the basis of the stress field intensity method, a theory of local stress-strain field for fatigue damage at notch is presented in this paper, which considers the effects of the local stress-strain' s gradient on fatigue damage. Through the finte element analysis on the elastoplasticity of notched specimen under the random alternate loading, a local stress-strain field intensity method is proposed for prediction of fatigue life under random loading. Using this method to predict the life of fatigue crack initiation has obtained better precision than the traditional local stress-strain method.