Performance indices and design charts can be used to quickly model and compare the structural efficiency of different shaped materials, layered systems and structural forms. This work presents a method for modelling the mass-efficiency of structures at the conceptual stage of design. The method is based on the concept of shape transformers, which describe dimensionless shape properties of a cross-section Shape transformers are size-independent and practical for defining classes of shapes in a way which is similar to the manner in which materials are classified. Used to formulate performance indices for lightweight shaped materials with arbitrarily scaled cross-sections and for plastic analysis of beams, shape transformers are conducive to visualize the effect of cross-section geometry and layer arrangement via material charts. These geometric operators help also to visualize the interaction between the selection of alternative structural forms and the choice of constituent member cross-section shapes. The method described here provides insight for engineers, students and educators involved in lightweight structural design.