A cutting tool including: a tool body (2) provided with an insert support seat (5) including a major seat surface (5a) that supports a bearing surface of a cutting insert, a plurality of seat side surfaces (5b, 5c) that supports side surfaces of the cutting insert at different positions, and a thinned portion (5d) continuous with the major seat surface and the seat side surfaces; and a cutting insert attached to the insert support seat, wherein a ridge at a position where the major seat surface and the thinned portion intersect, a ridge at a position where the seat side surface and the thinned portion intersect, and a ridge at a position where the thinned portions continuous with each other intersect are each formed of a convex arc curved surface.

A milling tool has a milling tool main element which has a first end with an interface for connection to a machine-side tool holder, and a free second end with at least one seat for receiving an exchangeable cutting insert. The following are arranged at the seat: a first support element for supporting a first side face of the cutting insert, which first support element is reversibly fastened to the milling tool main element by a first fastening element, a second support element for supporting a second side face of the cutting insert, which second support element is reversibly fastened to the milling tool main element by a second fastening element, and a third support element for supporting an underside of the cutting insert. The third support element is reversibly fastened to the milling tool main element by a third fastening element.