A method is presented for the prediction of optimal configurations for two-material composite continuum structures. In the model for this method, both local properties and topology for the stiffer of the two materials are to be predicted. The properties of the second, less stiff material are specified and remain fixed. At the start of the procedure for computational solution, material composition of the structure is represented as a pure mixture of the two materials. This design becomes modified in subsequent steps into a form comprised of a skeleton of concentrated stiffer material, together with a nonoverlapping distribution of the second material to fill the original domain. Computational solutions are presented for two example design problems. A comparison among solutions for different ratios of stiffness between the two materials gives an indication of how the distribution of concentrated stiffer material varies with this factor. An example is presented as well to show how the method can be used to predict an efficient layout for rib-reinforcement of a stamped sheet metal panel.