This paper presents a method for generating solutions to a class of conceptual design problems. We define conceptual design as the transformation of functional requirements to abstract physical systems in two stages: 1) phenomenological design — transforming a functional requirement to a behavior description by using physical principles; and 2) embodiment design — transforming the behavior specification to a physical embodiment that exhibit the required behavior. In order to reason about the behavior of in-progress designs, a new representation called behavior graphs has been defined. Behavior graphs are similar to bond graphs but have been developed as a design tool. (Bond graphs were developed as an analysis tool.) In order to guide the design process, the iterative redesign model of design is used at both the phenomenological and embodiment levels. The behavior graph representation and iterative redesign model constitute the conceptual design method presented here. A experimental computer program implementing this method is discussed and illustrative examples presented.