The elastic constant tensor of Sim / Gen superlattices with different modulation wavelengths has been determined by Brillouin light scattering spectroscopy. The C11 elastic constant obtained for Sin / Gen (where bilayers are built up by an equal number of Si and Ge monolayers) and Sin / Ge4n superlattices are 13% above the predictions of the continuum elasticity theory, using the Cij values of bulk Si and Ge. On the other hand, the elastic constant tensor of Si4n / Gen and Si3n / Gen superlattices matches perfectly the predictions. A structural analysis by extended x-ray absorption fine structure spectroscopy of the interfaces has been carried out and the unexpected different elastic behaviour can be explained by the observed strains at the superlattice interfaces.