We present a new method based on GPU acceleration for real-time transparency and translucency rendering. Our method computes refraction at both the front and back sides of a transparent object, as well as internal reflection, thus delivering interactive realistic transparency effects on a commodity PC. The real-time performance is made possible by a new acceleration data structure, called geocube, that enables the use of GPU for fast ray-surface intersection testing. In addition, within the same framework, we introduce the novel use of the mip-map for a hierarchical representation of a sequence of key prefiltered environment maps to simulate translucency. By taking ray depth into account and using GPU to interpolate the key filtered maps to produce the desired blurring effects, we achieve real-time realistic translucency rendering of slightly scattering media that allows show-through of background details.