In this work, we contribute to the description of macroscopic response of 304L stainless steel (SS) under cyclic straining and stressing tests at room temperature in the uniaxial and biaxial paths, and we diagnose their phenomenological macroscopic behavior . Material characterization is an important task for the fatigue assessment in mechanical engineering then, it is important to understand the anelasticity of the metals under stress and strain controlled tests.While, the uniaxial Ratcheting phenomenon responses is analysed under proportional loading path (tension-compression) and under opposite stress cycles which included, the influences of mean and amplitude stresses. It was demonstrated that the uniaxial Ratcheting depended on the hysteresis loop shape simulation. On the other hand the biaxial Ratcheting is tested under constant tension and shear stress. The results of the numerical simulation are obtained using the ZébuLon calculation code by opting for the Chaboche model.