According to the evolution of functional solving models, this paper first compares the characteristics and the consistency of the thinking process of three different functional solving models, including the extended function-environment-behaviour-structure (FEBS/e) model, the extended behaviour-driven function-environment-structure (B-FES/e) model, and the extended function-behaviour-implementation-environment (FBIE/e) model. Then, a new functional solving model with multiple elements and evolutions (FSMEE) is proposed. In this model, the reasoning process of product functional design is classified into 12 basic mapping relations by virtue of the regulation analysis of the design process. The evolutionary logic of basic mapping relations is then developed according to the optimal degree. In addition, the computer representation of the hierarchy design process is established by means of the topology relation matrices and adjacency relation matrices. Finally, an example of an emergency cut-off valve is presented to demonstrate the model's feasibility.