Materials, devices and methods for the treatment of congestive heart failure are disclosed. In these methods, the volume of the left ventricle is reduced, thereby increasing the efficiency of the pumping action of the heart. Volume reduction is accomplished by introduction of biocompatible materials into the wall of the left ventricle, or into the ventricle itself. Also disclosed is a method for ventricular geometry reduction wherein flexible, elastic bands are attached to the external surface of the heart to affect a decrease in the volume of the left ventricle. Other disclosed devices include catheters and elastic bands that are usable in these treatments. Finally, disclosed is a device having an anchor disposed proximate the heart's apex, a plurality of petals, and a tensioning band secured to at least one of the petals.