A cutting insert of an embodiment includes an upper surface including a first upper cutting edge and a second upper cutting edge, a lower surface including a first lower cutting edge and a second lower cutting edge, and a side surface. The side surface includes a first surface extending from the second upper cutting edge, a second surface extending from the first lower cutting edge, a third surface extending from the first upper cutting edge, and a fourth surface extending from the second lower cutting edge. The first surface and the fourth surface are parallel to a central axis. The second surface is inclined so as to depart from the central axis as going from the lower surface toward the upper surface. The third surface is inclined so as to depart from the central axis as going from the upper surface toward the lower surface.

A cutting element, which is configured for the machining of a non-metallic composite material composed of a matrix and particles held together by the matrix, has a flank face, a rake face and a cutting edge which is coated with an edge coating and via which the flank face and the rake face are connected to one another, with which the non-metallic composite material can be machined in an improved fashion. The cutting edge within a cutting edge section thereof is curved in such a way that the cutting edge immediately beneath the edge coating in a section in a section plane that is perpendicular to the cutting edge has, at every point of the cutting edge section, a local radius of curvature which is greater than or equal to 10 m and less than or equal to 80 m.