[en] An extensive study of the uniaxial cyclic material behavior of an AISI 304L austenitic stainless steel is proposed in the high cycle regime and in constant amplitude loadings. More particularly, the effect on the material behavior and lifetime of a mean axial stress is evaluated imposing either a stress or a strain amplitude. Almost no effect is observed on the stress fatigue curve while a reduction of about 30% is obtained on the strain fatigue curve in the endurance regime. It appears that a stress amplitude fatigue parameter or a Smith-Watson-Topper parameter predict accurately such differences based on the material behavior at maximum cyclic softening. (authors)