A brachytherapy appliance removably positionable on or against a surface of a living body, such as the body of a human or animal, for positioning a therapeutic delivery device in a desired precise location in relation to a selected portion of the body in or adjacent to the surface and containing a cancer, tumor, or other diseased tissue, for delivering a therapy, particularly radiation, to the diseased tissue, and a method of making the appliance so as to conform to the body surface, based on a computerized three dimensional model or map generated from a scan of the body region, the appliance being particularly adapted for use in a body cavity such as the oral cavity.