The calculation of elastic constants of Ag/Pd superlattice thin films by molecular dynamics simulations with many-body potentials is presented. It reveals that the elastic constants C11 and C55 increase with decreasing modulation wavelength A of the films, which is consistent with experiments. However, the change of C11 and C55 with A is found to be around the values determined by a rule of mixture using bulk elastic constants of metals.No supermodulus effect is observed and it is due to cancellation between enhanced and reduced contributions to elastic constants from Ag and Pd layers subjected to compressive and tensile strains, respectively.