an improved elastic band for ligating tissue within a living body comprises a central opening defining an axis . a first curved edge is formed between a first surface extending substantially parallel to the axis and a second surface extending substantially perpendicular to the axis . 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 .