A cutting insert includes opposing first and second major surfaces and two side surfaces extending therebetween, two side abutment surfaces, each located on a respective side surface and a clamping recess which opens out to the second major surface and/or to the insert front surface. The side abutment surfaces converge towards the first major surface and the side surfaces converge in a direction away from an insert front surface which extends between the major surfaces and the side surfaces. The clamping recess does not extend beyond a mid plane, which is located midway between the first and second surfaces.