A tangential cutting insert (1, 101) comprising: an insert body portion comprising a body portion upper surface, a body portion lower surface located opposite the body portion upper surface, and body portion side surfaces extending between the body portion upper surface and the body portion lower surface, the insert body portion including an axis defined therein which passes through the body portion upper surface and the body portion lower surface; and a plurality of projecting portions each comprising two cutting edges, each projecting portion provided integrally with the insert body portion at an outer position of the insert body portion in a direction orthogonal to the axis, wherein the projecting portion comprises a projecting portion upper surface connected to the body portion upper surface, a projecting portion lower surface connected to the body portion lower surface, two projecting portion side surfaces each connected to the corresponding body portion side surface, and a projecting portion side end surface extending therebetween, and the projecting portion comprises a round corner surface formed thereon and extending between the projecting portion upper surface and the projecting portion side end surface, wherein each of the two cutting edges is formed along a respective intersecting ridge portion between the related projecting portion side surface and each of the projecting portion upper surface, the round corner surface, and the projecting portion side end surface, so as to include a corner formed along an edge of the round corner surface and such that the projecting portion side surface serves as a rake face, and wherein with respect to each of the projecting portions, when a respective first plane is defined so as to contain the axis, the projecting portion is formed substantially plane-symmetrically with respect to the first plane, characterized in that the projecting portion is designed in such a manner that a length of the round corner surface extending in a direction orthogonal to the first plane is shorter than a diameter of an inscribed circle defined on the body portion upper surface, and wherein the round corner surface is formed to have the same or substantially the same curvature on any plane parallel to the first plane. an insert body portion comprising a body portion upper surface, a body portion lower surface located opposite the body portion upper surface, and body portion side surfaces extending between the body portion upper surface and the body portion lower surface, the insert body portion including an axis defined therein which passes through the body portion upper surface and the body portion lower surface; and a plurality of projecting portions each comprising two cutting edges, each projecting portion provided integrally with the insert body portion at an outer position of the insert body portion in a direction orthogonal to the axis, wherein the projecting portion comprises a projecting portion upper surface connected to the body portion upper surface, a projecting portion lower surface connected to the body portion lower surface, two projecting portion side surfaces each connected to the corresponding body portion side surface, and a projecting portion side end surface extending therebetween, and the projecting portion comprises a round corner surface formed thereon and extending between the projecting portion upper surface and the projecting portion side end surface, wherein each of the two cutting edges is formed along a respective intersecting ridge portion between the related projecting portion side surface and each of the projecting portion upper surface, the round corner surface, and the projecting portion side end surface, so as to include a corner formed along an edge of the round corner surface and such that the projecting portion side surface serves as a rake face, and wherein with respect to each of the projecting portions, when a respective first plane is defined so as to contain the axis, the projecting portion is formed substantially plane-symmetrically with respect to the first plane, characterized in that the projecting portion is designed in such a manner that a length of the round corner surface extending in a direction orthogonal to the first plane is shorter than a diameter of an inscribed circle defined on the body portion upper surface, and wherein the round corner surface is formed to have the same or substantially the same curvature on any plane parallel to the first plane.