This numerical study focuses on the recent observations of Man et al.  showing welloriented grains presenting no Persistent Slip Marking even if PSMs are observed in 86% of the surface grains in 316L austenitic stainless steel cycled at room temperature up to 60% of fatigue life. Scanning Electron Microscopy (SEM) permits us to build Finite Element (FE) meshes of the observed aggregates and to assign to the modelled grains the crystallographic orientations measured by Electron Back Scattering Diffraction (EBSD). Then, 3D FE computations using crystalline elasticity allow the evaluation of mean grain stress tensors and resolved shear stresses. The results could explain qualitatively the anomalous behaviour of the studied well-oriented grains which is partly due to the particular orientations and shapes of the neighbour grains. This study highlights the influence of crystalline elasticity and neighbour grains in microplasticity and crack nucleation.