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Embedded systems involve a coupling of hardware and software. Modeling of an embedded system is a key step in the requirements phase, when a product’s specifications are gathered and modeled. This paper focuses on the specification and modeling phase (the requirements phase) in systems that have been modeled using the FSM approach. The concept of state has been a central notion in this development. While FSM has many diverse and unique properties, the notion is not rich enough to capture complex systems, especially embedded systems with software and hardware parts. The concept of state raises misconceptions, especially in education. To provide an alternative to FSM for system description, this paper introduces a new model as the foundation for a new approach to modeling applications that need state-like methodology. The methodology is based on identifying “things that flow” (e.g., data, numbers, signals) and specifies their streams of flow in terms of no more than six generic stages. The resulting conceptual picture provides a map of diverse flow systems that trigger each other. In this paper, study cases that originally used FSM are re-diagrammed using the new methodology to compare the semantics reflected in each method. Such semantics can be used to understand the behavior of a given system in design and educational contexts. The results point to the viability of the flow-based method for capturing the specification and modeling of systems.