Abstract. In this paper we present PRISM-PSY, a novel tool that performs precise GPU-accelerated parameter synthesis for continuous-time Markov chains and time-bounded temporal logic specifications. We redesign, in terms of matrix-vector operations, the recently formulated algorithms for precise parameter synthesis in order to enable effective data-parallel processing, which results in significant acceleration on many-core architectures. High hardware utilisation, essential for performance and scalability, is achieved by state space and parameter space parallelisation: the former leverages a compact sparse-matrix representation, and the latter is based on an iterative decomposition of the parameter space. Our experiments on several biological and engineering case studies demonstrate an overall speedup of up to 31-fold on a single GPU compared to the sequential implementation.