This paper presents a new analytical method to estimate the thickness of an undeformed chip in ball-nosed end milling. It has been firstly pointed out that the geometric situations on the determination of the thick-ness are categorized in three cases based on the relationship among the milling parameters. Secondly each corresponding case has been reduced into a comprehensive equation with introducing a coordinate system of tool axis orientation. Thirdly "backward cutting" near the center of tool is pointed out that is irregular interference between the flank and the workpiece. So "backward cutting" occurs a non contact part on the cutting edge. And a condition of "backward cutting" has been clarfied. An area of "backward cutting" in a ball-nosed end mill is shaped circle that exists beside the center of tool axis.