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 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 (B) 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 (B) has at least a directional component (d1) normal to the first lateral seat surface and a directional component (d2) 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 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 (B) 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 (B) has at least a directional component (d1) normal to the first lateral seat surface and a directional component (d2) normal to the second lateral seat surface , and the supporting element has a protruding portion having a shape of a segment of a sphere. <EOS>