Function structures are used during conceptual engineering design to transform the customer requirements into specific functional tasks. Although they are usually constructed from a well-understood black-box description of an artifact, there is no clear approach or formal set of rules that guide the creation of function structures. To remedy the unclear formation of such structures and to provide the potential for automated reasoning of such structures, a graph grammar is developed and implemented. The grammar can be used by a designer to explore various solutions to a conceptual design problem. Furthermore, the grammar aids in disseminating engineering functional information and in teaching the function structure concept to untrained engineers. Thirty products are examined as a basis for developing the grammar rules, and the rules are implemented in an interactive user environment. Experiments with student engineers and with the automated creation of function structures validate the effectiveness of the grammar rules.