Discrete-event simulation (DES) is a widely used computational method in health services and health economic studies. Despite increasing recognition of the advantages of open, reusable DES models for both healthcare practitioners and simulation researchers, in practice very few authors share their model code alongside a published paper. In the context of Free and Open Source Software, this paper examines the practice of model and code sharing, and the disincentives and challenges, which include lack of time, reuse concerns, and knowledge barriers. We present a pilot framework to begin to address the opportunities and challenges of sharing DES models in healthcare called STARS: Sharing Tools and Artefacts for Reusable Simulations. STARS aligns with existing guidelines and documentation, including reproducibility initiatives, and enables computer models to be shared with users of differing technical abilities. We demonstrate the feasibility and applicability of STARS with three applied DES examples using Python. Our framework supports the development of open, reusable DES models which can enable partner healthcare organisations to preview, validate, and use models. Academic research teams can benefit from knowledge exchange, enhanced recognition and scrutiny of their work, and long-term archiving of models.