A harness for treating vessel aneurysms is disclosed. The harness applies elastic, compressive reinforcement on the aneurysm to reduce deleterious wall tension and to resist the shape change of the vessel. Rather than imposing a dimension beyond which the aneurysm cannot expand, the harness provides no hard limit over the range of systolic expansion of the vessel. Instead, the harness follows the contour of the vessel throughout systole and continuously exerts gentle resistance to stretch. Also disclosed is a method of delivering the vessel harness to the vessel with minimal invasion.