The process of sketching can support the sort of transformational thinking that is seen as essential for the interpretation and reinterpretation of ideas in innovative design. Such transformational thinking, however, is not yet well supported by computer-aided design systems. In this paper, outcomes of experimental investigations into the mechanics of sketching are described, in particular those employed by practicing architects and industrial designers as they responded to a series of conceptual design tasks. Analyses of the experimental data suggest that the interactions of designers with their sketches can be formalised according to a finite number of generalised shape rules. A set of shape rules, formalising the reinterpretation and transformations of shapes, e.g. through deformation or restructuring, is presented. These rules are suggestive of the manipulations that need to be afforded in computational tools intended to support designers in design exploration. Accordingly, the results of the experimental investigations informed the development of a prototype shape synthesis system, and a discussion is presented in which the future requirements of such systems are explored.