Abstract: Based on a series of uniaxial ratchetting tests of 304 stainless steel, the influences of four stresses (mean, amplitude, peak and valley) on saturated ratchetting (SR) strains are investigated. It is discovered that there exists a unique threshold for peak stress and SR strains vary monotonously with peak stresses. Peak stress, therefore, is an essential cause that leads to positive ratchetting deformation of materials. According to this phenomenon, the concepts of ratchetting threshold and ratchetting stress are proposed, and a saturated ratchetting model (SRM) for describing the constitutive relationship between SR strain and ratchetting stress is presented. The experimental results show that the history under previous low cyclic stresses has no effect on SR strains. This leads to the development of a single-specimen method to built SRM, with which a ratchetting test needs only one to three specimens with about ten different levels of peak stresses. The safety factor is between 1 and 1.3 for SRM to predict test results of SR strains for 304 steel specimens under stresses with only one level of peak stress.