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. Suitable biocompatible materials include those that undergo a phase transition within the ventricle or within the wall of the ventricle, and are thereby converted from a substantially liquid state to a substantially solid state. Such materials also include those which increase in volume during the transition from the liquid state to the solid state. Also disclosed is a method for ventricular geometry reduction wherein flexible, elastic bands are attached to the external surface of the heart to effect a decrease in the volume of the left ventricle. Finally, disclosed are devices including catheters and elastic bands that are usable in these treatments.