Fatigue crack initiates in the slip band and exists also in it near fatigue limit; many slip bands are apt to appear in the direction of the maximum shearing stress; crack propagates by the normal tensile stress; the maximum shearing stress on a plane at fatigue limit is reduced by the effect of the normal stress on the same plane. From these results of the experiment, a new criterion is proposed, which coincides with the Gough's empirical formula for the brittle materials under combined stress. As the plane of the maximum shearing stress is varied by the various combination of torsion and bending, the isotropic material should be used in the combined stress experiment. In this paper, the results of experiments on three isotropic and one anisotropic materials are discussed and compared with the criteria proposed up to the present.