A cutting insert includes an insert body having a polygonal plate shape. Rake faces are formed on polygonal surfaces of the insert body, and flank faces are formed on lateral faces of the insert body arranged around the polygonal surfaces. Main cutting edges are formed on side ridges of the polygonal surfaces at intersecting ridgelines between the rake faces and the flank faces. Each main cutting edge extends between two corners adjacent to each other in a circumferential direction of the polygonal surface among corners of the polygonal surface. When seen from a direction opposing the rake face, one end portion of the main cutting edge that stretches to one corner of the two corners has a convexly curved shape, and the other end portion of the main cutting edge that stretches to the other corner of the two corners has a concavely curved shape.

A cutting apparatus can include a cutting insert having at least one chip breaking mechanism. A chip breaking mechanism can include an elliptical hump supported by an inner rib. The elliptical hump can be positioned adjacent a corner of a cutting insert body, for example. The elliptical hump can also be positioned adjacent a tapered cutting edge and a plurality of grooves that include an outer groove and an inner groove that have different radiuses are spaced apart from each other by a lip, or step. Embodiments may also include a variable land positioned adjacent to an outwardly from the outer groove to facilitate chip breaking.