Abstract: In this paper, a geometric shadow mapping(GSM) algorithm is proposed to address the issues of shadow aliasing artifacts and depth bias in shadow mapping algorithm. In GSM, occluders are discretely represented in terms of the original triangles of the scene. Both perspective and projective aliasings can be greatly reduced due to the ac-curate reconstruction of the depth from continuous geometries. For a given scenario, a relatively small and constant depth bias can guarantee both faithful contact shadows and being free of the self-shadowing problem. Furthermore a GPU-based geometry buffer compression method is proposed to reduce the storage redundancy of triangles. Packet-based shadow evaluation is employed to further reduce the total memory fetch overhead of the algorithm. To remedy artifacts caused by inconsistent pixels, depth values are estimated via linear extrapolations for such pixels. The experimental results demonstrate that the proposed GSM algorithm can generate high-quality hard shadows in real time.