A finite element modeling is developed to simulate and visualize the discontinuous chip formation in the orthogonal cutting of 60 percent Cu-40 percent Zn brasses. A ductile fracture criterion expressed as a function of strain, strain rate and hydrostatic pressure is applied to the crack growth from the tool tip to the chip free surface in the segmentation of discontinuous chips. Chip shape and the inclination of fracture surface produced in computational machining are in good agreement with those in actual machining. The visualization of the computational machining processes clarifies the mechanism of discontinuous chip formation. The influences of chip segmentation upon the residual stress and strain in the machined layer are also clarified quantitatively.