With the aim of improving productivity in pocket machining the uncut regions are one of the most influencing factors on the tool path length and cutting time. We are interested in two kinds of uncut regions; the corner uncuts that appear between the passes and the center uncut. In this paper we have developed a new analytical model of tool path for machining pockets in 2½D with contour parallel offset for an arbitrary shape of pocket boundary whether line-line or line-arc. For the corner uncuts we propose a novel coefficient which ensures the ideal cover area between passes without letting behind any uncut region. For the center uncut we propose an automatically additional reduced looping with a passage segment that depends on the center uncut region geometry. For the purpose of the validation of this new developed method some selected numerical examples are presented. The obtained results show that our new approach minimizes both the tool path length and the machining time compared to other methods. Thus this new method offers an efficient contour parallel offset of tool path generation and an optimized machining.