Machine for diamond-finishing elongated bodies, which comprises: - a support structure; - at least one driving group, mechanically supported by said support structure and adapted to move an elongated body to be diamond-finished along a movement path; - at least one operating group, mechanically supported by said support structure, placed to intercept said movement path and provided with at least one diamond-finishing milling cutter adapted to operate on the elongated body; wherein said operating group comprises: - a support body mechanically connected to said support structure; - a rotatable support, which is rotatably connected to said support body around a first rotation axis and is provided with a through hole, which is crossed by said movement path and has an axis substantially parallel to said first rotation axis; wherein said diamond-finishing milling cutter is mounted on said rotatable support and projects inside said through hole towards said axis; - first motor means mechanically connected to said rotatable support and arranged for rotating said rotatable support around said first rotation axis; wherein said support body is provided with a housing opening extended in a through manner parallel to the axis of the through hole of said rotatable support; wherein said rotatable support has substantially annular shape and is mounted, in a rotatable manner, within the housing opening of said support body; said machine being characterized in that said rotatable support is provided with an inner annular surface, which is extended around said axis, perimetrically delimiting said through hole; wherein said diamond-finishing milling cutter is mounted on the inner annular surface of said rotatable support, projectingly extended from said inner annular surface within said through hole. - a support structure; - at least one driving group, mechanically supported by said support structure and adapted to move an elongated body to be diamond-finished along a movement path; - at least one operating group, mechanically supported by said support structure, placed to intercept said movement path and provided with at least one diamond-finishing milling cutter adapted to operate on the elongated body; wherein said operating group comprises: - a support body mechanically connected to said support structure; - a rotatable support, which is rotatably connected to said support body around a first rotation axis and is provided with a through hole, which is crossed by said movement path and has an axis substantially parallel to said first rotation axis; wherein said diamond-finishing milling cutter is mounted on said rotatable support and projects inside said through hole towards said axis; - first motor means mechanically connected to said rotatable support and arranged for rotating said rotatable support around said first rotation axis; - a support body mechanically connected to said support structure; - a rotatable support, which is rotatably connected to said support body around a first rotation axis and is provided with a through hole, which is crossed by said movement path and has an axis substantially parallel to said first rotation axis; wherein said diamond-finishing milling cutter is mounted on said rotatable support and projects inside said through hole towards said axis; - first motor means mechanically connected to said rotatable support and arranged for rotating said rotatable support around said first rotation axis; wherein said support body is provided with a housing opening extended in a through manner parallel to the axis of the through hole of said rotatable support; wherein said rotatable support has substantially annular shape and is mounted, in a rotatable manner, within the housing opening of said support body; said machine being characterized in that said rotatable support is provided with an inner annular surface, which is extended around said axis, perimetrically delimiting said through hole; wherein said diamond-finishing milling cutter is mounted on the inner annular surface of said rotatable support, projectingly extended from said inner annular surface within said through hole.