Abstract: The overall behavior of an elastic material with a periodic microstructure is governed by the microstructure whose effective properties are computed using a homogenization method. Improvements in materials performance can be obtained by designing new topologies of microstructures of these materials. The topology and volume fraction of the microstructure determines the effective properties of the materials. A multiple objective function model is presented to optimize the topology of the periodic microstructure with two or three-phase materials. A combination of effective elastic properties is maximized. Constraints on material volume fraction and perimeter control for eliminating the checkerboard are considered without the restriction of prescribed microstructure symmetry. By means of finite element method and convex programming techniques, several examples of optimal design of multiphase microstructures are solved. Influences of volume fraction, mesh dependence and elastic modulus ratio of three-phase materials on the optimal microstructures are discussed. Key words: topology optimization，microstructure design, multiphase materials, Multiple objective function