The elastic constant tensors of Si m /Ge n superlattices with different modulation wavelengths have been determined by Brillouin light scattering spectroscopy, and their Young's moduli measured by the nanoindentation technique. Two sets of samples have been studied: m ¼ n and m ¼ 4n. The C 33 elastic constant obtained for Si n /Ge n superlattices (where bilayers are built-up by an equal number of Si and Ge monolayers) are some 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 constants tensor of Si 4n /Ge n superlattices (where bilayers are built-up by four times more Si monolayers than Ge ones) matches perfectly the predictions. A thorough structural analysis by low-angle X-ray reflectivity, high-angle diffraction and X-ray absorption spectroscopy has been carried out and a deep characterization of the microstructure is presented here. The unexpected value of C 11 in Si n /Ge n superlattices can be attributed to the compressed Si-Ge alloy found at the wide interfaces present in that set of superlattices.