This paper describes a design process theory by axiomatic approach based on General design theory. Theorems under a hypothesis concerning real designers are deduced, and from it, a production rule type design process model is introduced. In this design process model, the design specification is decomposed into some concepts about physical rules, and the function elements, each of which actualizes the corresponding physical rule as an entity, are selected. The design specification is actualized by the combination of those function elements.In order to operate this design process, a good representation method for functions which enables the decomposition of the specification or the representation of the physical rules, is.required. In the present study, the pai-number method is developed, which is derived from the fact that a machine function can be expressed by the inputoutput energy relation. By using this pal-number method, a guiding principle for the rationalization and the construction of CAD systems of the conceptual design stage of machines is obtained.