The notion of a hybrid system is centered on a composition of discrete and continuous dynamics. Although the difficulty in modeling hybrid systems comes from the diversity of these systems, the most promising approach to mitigate this issue is developing expressive and precise modeling languages. Nevertheless, the developing of expressive and precise modeling languages does not necessarily mean the emergence of a new language, on the contrary, this paper proposes a precise semantics for a subset of existent languages.In this paper, we introduce hybrid fUML that blends synchronous features for controlling discrete behaviors, and differential algebraic equations (DAEs) into the standardized fUML (foundational subset for executable UML models). Synchronous features focused on discrete behaviors come from synchronous languages, which have been established as a technology of choice for specifying, modeling and verifying real-time systems, e.g., Lustre. Continuous behaviors are modeled using DAEs described using a subset of Modelica syntax. The subset of Modelica syntax is selected in such a way that its semantics is defined by the standard mathematical semantics.A case study considering a spring-mass-damper system was developed. Such systems address the control of structural vibrations (including aerospace structures) and it was modeled by a continuous spring-mass-damper plant and a discrete proportional controller.The main innovative contribution of hybrid fUML lies in the novel model of computation. The model of computation allows the synchronization of physical time at the environment and at the models, which enables determinism, predictability and straightforward composition of models of hybrid systems.