The enhanced generation of a spontaneous Raman signal by way of elastic scattering is demonstrated. Using Monte Carlo simulations, we show that elastic scattering, by increasing the path length of light through the medium, enhances the generation of a Raman signal. This is investigated over a large parameter space, demonstrating that this effect is robust, and providing additional physical insight into the dynamics of light propagation in a turbid medium. Both the temporal and spatial profiles of the Raman signal are shown to depend heavily on the amount of scattering present.