With the upcoming generation of telescopes, cluster scale strong gravitational lenses will act as an increasingly relevant probe of cosmology and dark matter. The better resolved data produced by current and future facilities requires faster and more efficient lens modelling software. Consequently, we present Lenstool-HPC, a strong gravitational lens modelling and map generation tool based on High Performance Computing (HPC) techniques and the renowned Lenstool software. We also showcase the HPC concepts needed for astronomers to increase computation speed through massively parallel execution on supercomputers. Lenstool-HPC was developed using lens modelling algorithms with high amounts of parallelism. Each algorithm was implemented as a highly optimised CPU, GPU and Hybrid CPU-GPU version. The software was deployed and tested on the Piz Daint cluster of the Swiss National Supercomputing Centre (CSCS). Lenstool-HPC perfectly parallel lens map generation and derivative computation achieves a factor 30 speed-up using only 1 GPU compared to Lenstool. Lenstool-HPC hybrid Lens-model fit generation tested at Hubble Space Telescope precision is scalable up to 200 CPU-GPU nodes and is faster than Lenstool using only 4 CPU-GPU nodes. (C) 2020 Elsevier B.V. All rights reserved.