A constriction device that constricts body tissue includes fixation structures for fixing the device on constricted body tissue. The device includes an elongated sleeve including an inner surface and opposed opened ends. The device is formed from expandable or elastic material so that when in an expanded condition, body tissue to be constricted may be received therein and thereafter, when released from the expanded condition, the body tissue is constricted by the device. The fixation structures include a plurality of fixation elements on the inner surface of the sleeve that grasp the body tissue upon release of the sleeve from the expanded condition to fix the device on the constricted tissue.