The Evolutionary Structural Optimisation (ESO) method is based on the simple concept that by slowly removing inefficiently used material from an over-designed structure, the residual shape of the structure evolves towards an optimum. The conventional ESO method has proven to be successful in generating optimum topologies, shapes and sizes for all kinds of structures. However, it mainly deals with isotropic and homogeneous materials. In optimum design of engineering structures, to efficiently use the available materials taking into account their behaviour in tension and compression, an extension of the conventional ESO method to the incorporation of tension/compression material has been proposed. The algorithms based on the principal stress criteria for optimisation of two-dimensional continuum structures are presented in this paper. In addition, two performance indices for tension- and compression-dominated designs are also developed. They can be used effectively to evaluate the structural efficiency of the various designs and to determine the optimum design topology. Practical design problems are solved using the proposed algorithms, including cable-stayed and arch bridge models. Numerical results indicate that the incorporation of tension/compression material is very effective in achieving tension- and compression-dominated designs. The optimum design has produced the structural shapes that make the best utilisation of the available materials.