Answer Set Programming (ASP) has become, the paradigm of choice in the field of logic programming and non-monotonic reasoning. Thanks to the availability of efficient solvers, ASP has been successfully employed in a large number of application domains. The term GPU-computing indicates a recent programming paradigm aimed at enabling the use of modern parallel Graphical Processing Units (GPUs) for general purpose computing. In this paper we describe an approach to ASP-solving that exploits GPU parallelism. The design of a GPU-based solver poses various challenges due to the peculiarities of GPUs' software and hardware architectures and to the intrinsic nature of the satisfiability problem.