This paper addresses a key theoretical problem in the mechanics of ultra-precision machining - shear angle prediction and cutting force variation induced by crystallographic anisotropy. The constitutive equation of crystal plasticity is implemented in the finite element modelling of the chip formation at micro-scale to take into account the effect of crystallographic orientations of the work piece to be cut. The theoretical prediction of shear angle and cutting force variation reveals two distinguished phases of pre-compression and steady-state cutting in ultra-precision diamond turning. The predicted patterns of cutting force variation are in good agreement with published experimental results. ; Department of Industrial and Systems Engineering