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Functional flow block diagrams (FFBDs) are a traditional tool of systems engineering and remain popular in some systems engineering domains. However, their lack of formal definition makes FFBDs imprecise and impossible to rigorously analyze. The inability to analyze FFBDs may allow specification errors to remain undetected until well into the system design process or, worse, until the system is operational. To help address these problems, we have developed a precise formal syntax and semantics for FFBDs, based on the application of metamodels and the process algebra Communicating Sequential Processes (CSP). FFBDs constructed within our formalized framework are precisely defined and amenable to analyses of properties, such as safety, progress, and conformance to required scenarios. We demonstrate some of the analyses made possible by our formalization in a simple case study of system specification and show how our formalization can be used to detect and correct subtle system errors during the specification phase.