A structure that can be used as a gastric band (and that may also have other uses as an implant elsewhere in a patient) includes a plurality of magnetic elements in a serial array that can be implanted so that the array extends in a circumferential direction around the patient's stomach (or other body tissue structure in the patient). Circumferentially adjacent magnetic elements magnetically attract one another to apply radial pressure to the tissue structure encompassed by the array, but those elements can also move apart in response to sufficient outward pressure from the encompassed tissue structure and/or the contents of (e.g., food in) that tissue structure. When used as a gastric band, the device can provide resistance to excessive food intake, which can help promote weight loss.