Attacks on a system often exploit vulnerabilities that arise from human behaviour or other human activity. Attacks of this type, so-called socio-technical attacks, cover everything from social engineering to insider attacks, and they can have a devastating impact on an unprepared organisation. In this paper we develop an approach towards modelling socio-technical systems in general and socio-technical attacks in particular, using timed automata and illustrate its application by a complex case study. Thanks to automated model checking and automata theory, we can automatically generate possible attacks in our model and perform analysis and simulation of both model and attack, revealing details about the specific interaction between attacker and victim. Using timed automata also allows for intuitive modelling of systems, in which quantities like time and cost can be easily added and analysed.