A tool system comprising: a holder having an insert seat for holding an exchangeable cutting insert, the insert seat having a base seat surface for supporting a lower side of the cutting insert, a first lateral seat surface for supporting a first lateral side of the cutting insert, and a second lateral seat surface for supporting a second lateral side of the cutting insert, the first and second lateral seat surfaces (23, 24) enclosing an internal angle (α) smaller than 180°, and an exchangeable cutting insert mounted in the holder via a clamping mechanism, the clamping mechanism comprising a clamp acting on an upper surface of the cutting insert and a fastening screw for tightening the clamp, wherein the upper surface of the cutting insert has an elongated clamping groove, wherein the clamp has a through-hole for receiving the fastening screw, at one side of the through-hole has two clamping protrusions engaging the clamping groove of the cutting insert at positions spaced from each other, and at the other side of the through-hole comprises a supporting element, wherein the holder has a guide surface guiding the supporting element in a backwards direction away from the cutting insert upon tightening the fastening screw, wherein the guide surface has a concavely curved shape, characterized in that the elongated clamping groove extends obliquely to both the first lateral seat surface and the second lateral seat surface, the backwards direction has at least a directional component normal to the first lateral seat surface and a directional component normal to the second lateral seat surface, and the supporting element has a protruding portion having a shape of a segment of a sphere. a holder having an insert seat for holding an exchangeable cutting insert, the insert seat having a base seat surface for supporting a lower side of the cutting insert, a first lateral seat surface for supporting a first lateral side of the cutting insert, and a second lateral seat surface for supporting a second lateral side of the cutting insert, the first and second lateral seat surfaces (23, 24) enclosing an internal angle (α) smaller than 180°, and an exchangeable cutting insert mounted in the holder via a clamping mechanism, the clamping mechanism comprising a clamp acting on an upper surface of the cutting insert and a fastening screw for tightening the clamp, wherein the upper surface of the cutting insert has an elongated clamping groove, wherein the clamp has a through-hole for receiving the fastening screw, at one side of the through-hole has two clamping protrusions engaging the clamping groove of the cutting insert at positions spaced from each other, and at the other side of the through-hole comprises a supporting element, wherein the holder has a guide surface guiding the supporting element in a backwards direction away from the cutting insert upon tightening the fastening screw, wherein the guide surface has a concavely curved shape, characterized in that the elongated clamping groove extends obliquely to both the first lateral seat surface and the second lateral seat surface, the backwards direction has at least a directional component normal to the first lateral seat surface and a directional component normal to the second lateral seat surface, and the supporting element has a protruding portion having a shape of a segment of a sphere.