Engineering Cyber-Physical Systems faces many challenges including the demand to integrate many different forms of functionalities and features. Traditional engineering processes are structured by the physical components and software modules of the final system and the engineering activities are concerned with evolving these components. In these approaches, the information, which components realize which functions and, in particular, which components interact in which way to implement a function, most often remains implicit. This hinders not only the collaboration of experts from different domains but also an agile approach to engineering which becomes efficient through automation, e.g. of V&V tasks. The shift towards functional requirements gives rise to a conceptual gap between their abstract descriptions and the very detailed descriptions of the system’s implementation. So far, the involved engineering domains have established an understanding of what a system’s function is, but these understandings have not been consolidated and integrated in a suitable interdisciplinary modeling technique. Therefore, we propose a functional development paradigm that promotes development by finding realizations of cyber-physical functions, which transform energy, matter, and data, rather than implementing physical products or software modules directly. Therein, we model a \cps as a network of interacting timed stream processing functions, which specify the desired logical behavior and the physical behavior. By applying this modeling technique to formalize the design process in mechanical engineering, we show how to integrate the functional understanding of software and mechanical systems, which paves the way for agile and holistic model-driven engineering of CPSs.