Abstract: Fatigue limit is a very important property of engineering materials in applications, but it is not a constant of material in fact. It is well known that a fatigue limit is dependent on fatigue cyclic properties, especially on either mean stress or maximum stress amplitude. Since the S-N curve corresponding to low stress amplitudes is strongly influenced by a fatigue limit, the quantitative and intrinsic relationship of a fatigue limit with mean stress is necessary for the life design in engineering applications. However, the classical experience relationships generally can only give a very rough estimation, thusly special experiments are usually necessary to obtain experimental results to meet engineering needs. This paper proposes a functional relationship to describe the variation of a fatigue limit with mean stresses. It is found that this relationship can well express the fatigue limits under different mean stresses for various engineering materials, and contains only three material constants. When these three material constants have been pre-determined, the fatigue limit for any fatigue cyclic loadings can be determined quantitatively. This functional relationship is referred to as the state relationship of fatigue strength, which is an intrinsic relationship of material property.