Elastic scattering between composite nuclei at high energy is studied on the basis of Glauber's multiple scattering formalism. As the mass number increases, the contribution from various multiple scatterings becomes appreciable and the terms corresponding to particular interaction processes play dominant roles at large angles in differential cross section. In the case of deuteron-deuteron scattering the comparison with experiment is done. The ratio of the real part to the imaginary one of scattering amplitude is considered. Comments are given on the effect of nuclear inner correlation, and it is shown that its· effect is less important even at large momentum transfer.