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The three-dimensional elastic-plastic stress fields around the notch have been analyzed by a crystallographic finite element program, which takes the effects of lattice rotation and finite deformation into consideration. The primary orientation is fixed along the [001] direction while the notch directions are parallel to [010] and []. The special attention is paid on the activating characteristic of slip systems. The numerical results show that the randomness orientations have important consequences on the activation of slip systems and the maximal resolved stress for the notch. The extreme of the maximum resolved stress appears around β=45o. The maximum resolved stress has an obvious fluctuation along the thickness direction, which is nearly constant in the midsection and tends to decrease sharply near the free surface. We can conclude that the slip (crack) is likely initiated at the midplane first. In the experiment, these regions correspond to the smooth region and the shear lip on the fracture face