This paper introduces a rigorous framework for function modeling of complex multidisciplinary systems based on the system state flow diagram (SSFD). The work addresses the need for a consistent methodology to support solution-neutral function-based system decomposition analysis, facilitating the design, modeling, and analysis of complex systems architectures. A rigorous basis for the SSFD is established by defining conventions for states and function definitions and a representation scheme, underpinned by a critical review of existing literature. A set of heuristics are introduced to support the function decomposition analysis and to facilitate the deployment of the methodology with strong practitioner guidelines. The SSFD heuristics extend the existing framework of Otto and Wood (2001) by introducing a conditional fork node heuristic, to facilitate analysis and aggregation of function models across multiple modes of operation of the system. The empirical validation of the SSFD function modeling framework is discussed in relation to its application to two case studies: a benchmark problem (glue gun) set for the engineering design community; and an industrial case study of an electric vehicle powertrain. Based on the evidence from the two case studies presented in the paper, a critical evaluation of the SSFD function modeling methodology is discussed based on the function benchmarking framework established by Summers et al. (2013), considering the representation, modeling, cognitive, and reasoning characteristics. The significance of this paper is that it establishes a rigorous reference framework for the SSFD function representation and a consistent methodology to guide the practitioner with its deployment, facilitating its impact to industrial practice.