A multi-grooving tool holder for holding cutting members seated in a side-by-side formation in a clamping portion of the holder. The clamping portion includes an upper clamp and a lower clamp and an elastic member is located in one of the upper and lower clamps. When cutting members are assembled in the clamping portion, the elastic member engages the cutting members and aligns each cutting member independently, by applying a force, and consequently a moment on the cutting members.