An EAS marker includes a rigid bottom piece of molded plastic having the shape of an open rectangular box. An elongated resonator is disposed in the bottom piece, the resonator being bowed downwardly about its longitudinal axis. A rigid separator of molded plastic is positioned over the open top of the bottom piece, thereby loosely encasing the resonator in the bottom piece. The method of making the EAS marker is preferably automated, with the top piece, the bottom piece and the separator being manufactured by rotary extrusion molding as part of a continuous web. The various continuous webs are automatically laminated to one another at nips between pairs of rollers.