In the diamond turning of brittle materials, the chip removal process can be classified into the following two types. One is the process due to plastic deformation on the characteristic slip plane and the other is due to cleavage fracture on the characteristic cleavage plane. Plastic deformation takes place in the work-material in front of the cutting edge when the resolved shear stress in the easy-slip direction exceeds a certain critical value inherent to the work-material before cleavage takes place. On the other hand, cleavage takes place when the resolved tensile stress normal to the cleavage plane exceeds a certain critical value before slip. In other words, the ductile and brittle mode of deformation can occur in the same material and transition between them can be obtained by changing the scale or the rate of operation. The type of chip removal process is determined by the predominant criterion in a particular cutting condition. When a plastic deformation process is prior to a cleavage, a very smooth and fine surface can be obtained. Contrarily, a cleavage process causes a cloudy surface that is covered with residual cracks. Therefore, there can be a critical condition of the stress field to determine whether a chip is removed by either a plastic deformation or a cleavage process. In general, the cutting force is an important factor affecting the size of the stress field and the scale of deformation. Under the same deformation conditions, a small cutting force makes the plastic deformation occur more easily. Reducing the cutting force is believedto be an effective measure for increasing the critical depth of cut.