A conical reamer having an elongated, longitudinally tapering head formed with two longitudinal flutes and rotated about its longitudinal axis by an integral shank portion. An axially elongated groove continuously adjacent each flute is open in a forward, and closed in a rearward direction and receives an axially elongated, reversible cutting blade having a cutting edge exposed in the flute. A frontal end face of the blade diverges obliquely from a plane perpendicular to the reamer axis at one acute angle in a radial direction toward the axis, and at a second acute angle in a direction circumferential relative to the axis. The end face is conformingly engaged in area contact by an abutment face of a clamping ring under the pressure of a clamping screw on the head.
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