This study deals with the investigation of the cyclic behaviour of 316L and 304L austenitic stainless steels in oligocyclic fatigue under biaxial loading. As a first step, we investigated the prediction of the character of 316L steel under imposed stress, by the fixation of a stress and the evolution of another, forming a cross-proportional loading path in a range of stresses. In addition, the analysis of the behavior of steel 304L with respect to the bi-axial union (primary and secondary loadings) was studied in order to produce the ratcheting phenomenon induced by the non-zero mean stress, governing the structure to damage in two opposite directions, diagonally symmetrical. An appreciable confrontation of the intrinsic characters of the two steels under the same loading conditions was discussed in the last intervention, controlled in strain, generating the phenomenon of cross-hardening and imposed stress. Producing the progressive strain that manifests itself at each loading cycle will make it possible to quantify the degree of plasticity of each material and optimize the most relevant steel. In this numerical study, the Chaboche model is selected, which is based mainly on perfect predictions and robust constitutive laws capable of reproducing observed macroscopic phenomena. All the simulations were carried out using the ZéBulon computation code. A lot of work on the behavior of 304L and 316L stainless steel has been carried out by several researchers in recent years. The results of previous experiments and numerical simulations have been compared to the results of this study, and a good match has been found.