A method of positioning an arcuate device against the inner walls of the disc, and particularly on the posterior and postero-lateral portions of the inner annulus of the disc. The arcuate device retains its predetermined arcuate shape when no pressure or force is applied to the catheter. In an embodiment, an arcuate cutter is used to remove tissue from the inner annulus of the disc. In another embodiment an arcuate device is used to progressively remove material from the interior of the mammalian intervertebral disc. In yet another embodiment, an arcuate device is used to remove the entire intervertebral disc and place supports to maintain a disc space.