The elastic constant tensor of Si-m/Ge-n superlattices with different modulation wavelengths has been determined by Brillouin light scattering spectroscopy. The C-11 elastic constant obtained for Si-n/Ge-n (where bilayers are built up by an equal number of Si and Ge monolayers) and Si-n/Ge-4n superlattices are 13% above the predictions of the continuum elasticity theory, using the C-ij Values of bulk Si and Ge. On the other hand, the elastic constant tensor of Si-4n/Ge-n and Si-3n/Ge-n 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.