Fatigue life of polycrystalline materials is mainly governed by the early stages of surface short cracks. Initiation and micropropagation phases, which represent from 50% to 80% of total component life, are experimentally proven to depend on material microstructure. The aim of this numerical study is to highlight the influence of local parameters (e.g. crystallographic orientation) on the short crack initiation. Finite element computations are performed with a crystal plasticity model. The investigations are carried out on 316L Stainless Steel with different fatigue loadings and various surface roughnesses. A qualitative study of volumetric strain localization is carried out to distinguish uniaxial and biaxial results. The slip plane activity in surface grains is characterized. Many configurations are tested to provide a statistical point of view. Results revealed the strong vulnerability of surface grains with a high Schmid factor on systems that produce extrusions. It is also demonstrated that taking account of geometrical singularities can strongly change the plastic strain localization due to crystal orientation.