Abstract: Instead of adopting the common idea of using volumeconstraint in topology optimization, this work is focused on the topologyoptimization of structures designed with multiphase materials and massconstraint. Related structural optimization models involving mass constraintand material interpolation model are proposed. Based on the study of twotypes of material interpolation models, i.e. GSIMP and UIM, the former isfound to introduce the nonlinearity into the mass constraint which bringsnumerical difficulties in searching the global optimum of the optimizationproblem. The adopted UIM model, however, makes the mass constraint linearand design variable separable, which favors the mathematical programmingapproaches, especially the convex programming methods. Numerical examplesshow that the presented scheme is reliable and efficient to deal with thestructural topology design problems of multiple materials with massconstraint. The mass constraint is proved to be more significant andimportant than the volume constraint in structural topology optimization.