We have measured the elastic properties of silica aerogels with densities in the range 0.1 to 0.4 g/cm3. The static Young's modulus E was obtained from three-point flexion experiments, while Brillouin scattering allowed the determination of the elastic constants C11 and C44, at hypersonic frequencies. The comparison of these frequency-dependent determinations shows that the samples exhibit large scale homogeneity down to a few μm. The density dependence of the Young's modulus and elastic constants is shown to obey the same power dependence pα with α = ∼- 3.8. The ratio of the compressibility to the shear modulus is similar to that found in bulk vitreous silica. Percolation models are used for the discussion of these elastic behaviour. © 1987 Elsevier Science Publishers B.V.