An elastic band for ligating tissue within a living body comprises an inner tissue engaging surface which, when in an operative position within the body, surrounds and directly contacts the tissue. At least a portion of the inner tissue engaging surface defines a plurality of discontinuities formed by one of projections and depressions. A method of ligating tissue within a living body using such a ligating band comprises the steps of positioning the elastic band, which has been stretched to increase the size of a central opening extending therethrough, adjacent to a portion of tissue to be ligated. The tissue to be ligated is then drawn through the central opening of the elastic band and the elastic band is released so that the size of the central opening decreases to grip the tissue received therein.