The brush seal includes manually-flexible, plastic-containing, brush-seal bristles attached to an elongated bristle holder. The rotary machine has a rotor and stator casing segments with segments of the brush seal positioned one each in a surface groove of a corresponding stator casing segment. In one example, the bristle holder is manually flexible, the bristles and the bristle holder define a monolithic unit, and the brush seal is coiled onto a spool from which a desired length is cut thereby avoiding the necessity of manufacturing a brush seal segment to a specific radius and a specific circumferential length to match a particular stator casing segment.