A cutting insert having four symmetrically located cutting edges is mounted on a cutting insert holder, which is in turn mounted on a rotary driver. One of the cutting edges projects out from the cutting insert holder. The rotary driver rotates the projecting cutting edge along a circular path. A tube end to be finished is held in contact with projecting cutting edge being colinear with the centerline of the tube. A plurality of cutting insert holders each has a cutting insert mounted thereon with the respective projecting cutting edges being located at varying distances from the axis of rotation. The design of the cutting edges also varies. Tube ends having different radii, wall thicknesses, cross section, or chamfers are finished by successively mounting on the rotary driver the cutting insert holders having projecting cutting edges located the required distances from the axis of rotation and having the appropriate designs.