Using digital twins, physical manufacturing objects can be virtualized and represented as digital models which are seamlessly integrated in both the physical and the digital space. This allows to simulate, verify and optimize production systems, from the logistical aspects to the manufacturing process and the involved components. A key challenge, in this area, is how to describe digital twins in complex manufacturing systems such that all physical details, processes, and verification needs are modeled at an appropriate and efficient abstraction level, e.g., modeling and detecting divers faults in production processes. To address this challenge, in this paper we present our work on modeling digital twins of manufacturing facilities using UML. UML class diagrams are used to describe static dependencies between entities, as well as to monitor and analyze the dynamic verification and quality aspects of manufacturing such as fault detection and consistency checks. Utilizing the key relevant features of UML in our approach, the designed class diagrams are used and enriched with behavioral models serving as digital twins which can be updated by live data from the manufacturing plant. We present a small example based on simulation programs and a demonstrator. The presented modeling approach and example provide useful insights to UML-based design of digital twins in complex manufacturing systems.