Most of structural components resisting to high cycle fatigue are subjected to a multiaxial state of stress. Since fatigue cracks generally initiate and propagate in a plane of maximal shear stress (stage I), the first approaches of Crossland and Sines considered the octahedral plane and their criteria are based on the amplitude of the second invariant of the deviatoric stress tensor. In order to take into account the mean stress, these authors postulated also a linear combination of
and the hydrostatic part of the stress tensor. It is now widely recognized that under high cycle loadings conditions, metals fracture is the result of the strain localization in some unfavorably oriented grains undergoing plasticity. Dang Van, followed by Papadopoulos and others, had proposed a multiscale framework which leads to a sufficient condition for non nucleation of cracks under high cycle loading. This condition is ensured by elastic shakedown at the grain scale (see the representive elementary volume on Fig. 1). Nevertheless, microplastic activity alone cannot explain the role of pressure on the fatigue limit and a generalized multiaxial fatigue limit depending on the hydrostatic pressure is due. So far, this is the proposal already suggested by Papadopoulos in his generalized multiaxial fatigue limit.