Abstract The shape and topology optimization of structures as an optimal density distribution problem is considered. An artificial material model, whose elastic moduli are contrived to stay close to the lower side of the Hashin-Shtrikman bounds, is introduced to obtain the efficient relationship between the effective elastic moduli and the density of the given material. The introduction of the new model results in optimal density distribution which is readily applicable to real structural patterns with the least possible porous regions. Also, a density redistribution algorithm is suggested in order to suppress checker-board patterns without the use of the higher order elements. This algorithm combined with the new artificial material introduced is shown to effectively work in extracting the optimal structure shape from the computed density distribution.