A model to calculate the Raman response of small Si crystallites immersed in an amorphous Si matrix is developed. The structure of the system is modelled by an infinite crystalline slab of varying width, in which the atoms on the (111) surfaces on both sides of the slab are attached to Bethe lattices. The Raman response is obtained from a simple polarisability model using the Green function technique. The results are compared with recent experiments. The model can be used for Si crystallites with free and hydrogenated (111) surfaces.