Cochleates, prospective nanoscale drug delivery vehicles, are rolls of negatively charged phospholipid membrane layers. The membrane layers are held together by calcium ions; however, neither the magnitude of membrane interaction forces nor the overall mechanical properties of cochleates have been known. Here, we manipulated individual nanoparticles with atomic force microscopy to characterize their nanomechanical behavior. Their stiffness (4.2-12.5 N/m) and membrane-rupture forces (45.3-278 nN) are orders of magnitude greater than those of the tough viral nanoshells. Even though the fundamental building material of cochleates is a fluid membrane, the combination of supramolecular geometry, the cross-linking action of calcium, and the tight packing of the ions apparently lead to extreme mechanical resilience. The supramolecular design of cochleates may provide efficient protection for encapsulated materials and give clues to understanding biomolecular structures of similar design, such as the myelinated axon.