A cutting insert having a generally polygonal tabular form, includes a main cutting edge formed along at least one of the ridges or edges of the upper and lower surfaces which oppose each other in the direction of the thickness of the tabular form, and a face connected to the main cutting edge is formed on the flank or flanks which surround and define the upper and lower surfaces. The face includes a convex curved surface and an angle of intersection between the convex curved surface and one of the upper and lower surfaces progressively changes. The angle of intersection between the convex curved surface and one of the upper and lower surfaces progressively increases or decreases along the length of the face from the face end adjacent to a free end of the tool to a face end adjacent to the base end of the tool. In a preferred embodiment, a flat surface is disposed on each side of the convex curved surface and each flat surface intersects one of the upper and lower surfaces at a constant angle. The flat surface adjacent to the face end adjacent to the free end of the tool intersects with one of the upper and lower surfaces at an angle which is greater or smaller than the angle of intersection between the flat surface adjacent to the face end adjacent to the base end of the tool and one of the upper and lower surfaces of the cutting insert.