Heat and mass transfer in macellular materials signifies an important topic of research for a range of advanced applications such as in thermal, aerospace, geotechnical and scaffold tissue engineering etc. Based on the mathematical similarity of various transport problems, this paper proposes a modified bidirectional evolutionary structural optimization (BESO) method for design of biphasic microstructural composites with desirable transport properties. The cellular materials considered herein comprise periodic base cells and the homogenization technique is adopted to determine their effective (bulk) properties. The key is to optimize the topology of base cell model for minimizing the difference between the effective and target transport properties. Numerical examples agree well with the well-known benchmarking microstructures and some of them are prototyped using biphasic solid free-form fabrication (SFF) technology. To facilitate comprehension of the algorithm, a short MATLAB program is provided in the Appendix. (C) 2012 Elsevier Ltd. All rights reserved.