The elastic properties of superlattices are strongly affected by strains in these materials. Elastic anomalies have been found in Nb/Cu, Mo/Ni, V/Ni, and Au/Cr superlattices. The strains measured with x rays explain quantitatively the elastic softening in Mo/Ni. An extension of these arguments explains not only the softening of Nb/Cu but the hardening and softening observed in Au/Cr. The origin of the strains is not known at the present time.