The attribute grammar formalism in engineering design is a new approach, suggested by Mullins and Rinderle [Mullins-91, Rinderle-91], to develop automated design tools to be used in the preliminary mechanical engineering design phase. This approach is based on the paradigm of gradual refinement of the design alternatives from an abstract form to a concrete design using transformation rules and associated engineering attributes. The characteristics of this approach are studied in the context of mechanical design problems requiring representation of and reasoning with shapes in the preliminary design phase. The design of extruded table legs is chosen as being representative of such design problems. The attribute grammars are found to be useful design and designer assistant tools in this context for various reasons. Attribute grammars provide a systematic and formal methodology to engineering design which is particularly useful in the preliminary design phase. Attribute grammars support a natural integration of the concept generation and selection phases with the detail design phase which have traditionally been treated very differently. Attribute grammars also support a decision making process which naturally combines constraints representing various aspects of design such as performance, manufacturing, geometry etc. The results show that the attribute grammars can can be used to represent and reason about the shapes. However, the specific grammar used to develop the alternatives for the extruded legs does not guarantee the optimality of the solution.