Illumination effects in translucent materials are a combination of several physical phenomena: absorption and scattering inside the material, refraction at its surface. Because refraction can focus light deep inside the material, where it will be scattered, practical illumination simulation inside translucent materials is difficult. In this paper, we present an a Point-Based Global Illumination method for light transport on translucent materials with refractive boundaries. We start by placing volume light samples inside the translucent material and organising them into a spatial hierarchy. At rendering, we gather light from these samples for each camera ray. We compute separately the samples contributions to single, double and multiple scattering, and add them. Our approach provides high-quality results, comparable to the state of the art, with significant speed-ups (from 9× to 60× depending on scene complexity) and a much smaller memory footprint.