The elastic constants of magnetic flux-line lattices in copper oxide superconductors have remained uncharacterized despite their essential role in determining important phenomena such as melting. Here the absolute values of the elastic moduli of flux-line arrays have been probed by correlating the positions of individual flux lines emerging from opposite sides of Bi2Sr2CaCu2O8 (BSCCO) superconductors. These experiments demonstrate that the compressional and shear moduli of the flux-line lattice are three orders of magnitude smaller than the values predicted by standard models. The origin of these changes in the moduli and the general applicability of this approach to other materials are discussed. In addition, there is a remarkable correspondence between the excitations of the flux-line arrays and those of superfluid helium.