A numerical study of the nano-indentation of the AZ31 alloy was performed in order to analyze the stress fields at the onset of twinning. The model considers indentation of the (101¯0) and (12¯10) planes by a spherical indenter with radii of 5, 10 and 50 μm. Material behavior is described by a crystal plasticity constitutive model with three critical resolved shear stresses for different slip modes. The CRSS values were obtained by fitting to experimental load-displacement curves. The stress and strain distributions are analyzed with a view to understanding twin initiation. The twins initiate during indentation at the stress level order of magnitude higher compare to uniaxial tests.