Content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence. ; We report on stress induced changes in the dispersion relations of acoustic phonons propagating in 27 nm thick single crystalline Si membranes. The static tensile stress (up to 0.3 GPa) acting on the Si membranes was achieved using an additional strain compensating silicon nitride frame. Dispersion relations of thermally activated hypersonic phonons were measured by means of Brillouin light scattering spectroscopy. The theory of Lamb wave propagation is developed for anisotropic materials subjected to an external static stress field. The dispersion relations were calculated using the elastic continuum approximation and taking into account the acousto-elastic effect. We find an excellent agreement between the theoretical and the experimental dispersion relations. ; The authors acknowledge financial support from the FP7 project MERGING (grant no. 309150); the Spanish MICINN projects nanoTHERM (grant no. CSD2010-0044) and TAPHOR (MAT2012-31392). JGB gratefully acknowledges support from the Spanish government through a Juan de la Cierva fellowship. MP and AS acknowledge funding from the Academy of Finland (grant no. 252598). ; Peer Reviewed