Fault Injection (FI) is a well-known system verification technique, in which faults are artificially introduced into a system, to assess its behavior in exceptional conditions. FI can be applied at different levels, including physical, hardware and software. FI has also been applied at model level, although the amount of work in this direction is limited. However, the importance of models in the development of complex systems is growing, pushing towards model-level verification and simulations. The Foundational UML (fUML) is a specific subset of UML, released as an OMG standard, that has a precise execution semantics and can therefore be executed. In this paper we investigate the application of FI to executable models specified with fUML. We first characterize the kind of fault that may be applied to fUML models, and then we realize an injection mechanisms based on automated model transformation. We apply the methodology to a simple example in the space domain, adapted from a real satellite system. We believe this is an important first step for the adoption of FI techniques on fUML models, for an early detection of design flaws. We conclude discussing some challenges and directions for future work.