We report a theoretical study of stimulated Brillouin scattering (SBS) in general anisotropic media, incorporating the effects of both acoustic strain and local rotation. We apply our general theoretical framework to compute the SBS gain for layered media with periodic length scales smaller than all optical and acoustic wavelengths, where such composites behave like homogeneous anisotropic media. We predict that a layered medium composing nanometer-thin layers of silicon and As2S3 glass has a bulk SBS gain of 1.28×10-9 W-1 m. This is more than 500 times larger than that of silicon and almost double the gain of As2S3. The enhancement is due to a combination of roto-optic, photoelastic, and artificial photoelastic contributions in the composite structure.