Abstract: The advent of GPUs with their ever-growing amount of parallel horse-power makes them a tempting resource for numerical computation. This is even truer with the new APIs for GPUs that recently appeared. These APIs (CTM from ATI and CUDA from NVidia) give a direct access to the multithreaded computational resources and associated memory bandwidth. A wide class of geometry processing methods needs to solve a linear system, where the non-zero pattern of the matrix is dictated by the connectivity matrix of the mesh. As a consequence, the existing dense and band-matrix solvers for the GPU cannot be used. In this paper, we introduce the CNC (Concurrent Number Cruncher), a general symmetric sparse system solver. Our CNC combines recent GPU programming techniques with supercomputing algorithms and data structures (namely block compressed row storage and register blocking). We demonstrate our solver implemented with CTM and applied to various geometry processing problems (parameterization and smoothing). We obtain a 5x acceleration factor as compared to a leading-edge CPU implementation (MKL).