Contemporary ergonomics problems are increasing in scale, ambition, and complexity. Understanding and creating solutions for these multi-faceted, dynamic, and systemic problems challenges traditional methods. Computational modelling approaches can help address this methodological shortfall. We illustrate this potential by describing applications of computational modelling to: (1) teamworking within a multi-team engineering environment; (2) crowd behaviour in different transport terminals; and (3) performance of engineering supply chains. Our examples highlight the benefits and challenges for multi-disciplinary approaches to computational modelling, demonstrating the need for socio-technical design principles. Our experience highlights opportunities for ergonomists as designers and users of computational models, and the instrumental role that ergonomics can play in developing and enhancing complex socio-technical systems. Recognising the challenges inherent in designing computational models, we reflect on practical issues and lessons learned so that computational modelling and simulation can become a standard and valuable technique in the ergonomists' toolkit. Practitioner summary: This paper argues that computational modelling and simulation is currently underutilised in ergonomics research and practice. Through example applications illustrating the benefits, limitations, and opportunities of such approaches, this paper is a point of reference for researchers and practitioners using computational modelling to explore complex socio-technical systems.