Finite element models in orthogonal cutting are presented to examine the influences of exit angles of the workpiece, tool rake angles, and backup materials on burr formation processes in 304 L stainless steel in particular. Based on the metal-cutting simulation procedure proposed by the authors, a series of stress and strain contours and final burr/breakout configurations are obtained. The burr formation mechanisms with respect to five different exit angles are found, and duration of the burr formation process increases with an increase of exit angle, resulting in different burr/breakout configurations. Based on the development of neg. shear stress in front of the tool tip, the tool tip damage, what is called "chipping," is investigated. Also, with fixed cutting conditions and workpiece exit geometry, the influence of the rake angle is found to be closely related to the rate of plastic work in steady-state cutting because the larger the rate of plastic work in steady-state cutting, the earlier the burr initiation commences. Furthermore, to effectively minimize the burr size, three cases of backup material influences on burr formation processes are examined It is found that the burr size can be effectively minimized when the backup material supports the workpiece only up to the predefined machined surface.