Advanced digital technology is finding its way into industrial production and control systems. This led to development of further concepts such as digital shadow and digital twin. In the former an accurate model of the cyber-physical system (CPS) is used to monitor it virtually, while the latter provides a possibility to adapt the CPS’s behavior. These developments are often welcome from the operators perspective, however they also pose new challenges in terms of cyber security: an operator could be led to believe the system is operating correctly due to the represented digital image while the CPS is under a cyber attack. In this paper we investigate several cyber security challenges of the digital twin technology and discuss potential mitigations for these challenges based on well established practices within the area of industrial control systems. We further describe the potential cyber attacks and mitigations using a semi-formal notation based on problem frames, we suggest in order to simplify the communication about cyber security challenges of digital twins between different stakeholders. This is shown within a context of a small case study. Finally we outline areas of research for the development of secure digital twin technology.