Extruded polystyrene rigid foams have attracted a great attention as a superior loadbearing thermal insulation material since their implementation in building construction. One of the most common application areas of this type of thermal insulation material is under raft foundations, where the foam normally undergoes high levels of compression loads. The purpose of this research is to determine how to simulate and optimize the structural response of extruded polystyrene under compression stresses. The optimization has been achieved through investigating the relation between the foam microstructure and the global mechanical properties. The foam was first examined using X-ray tomography imaging technique to acquire some morphological information about the microstructure. The obtained morphological data of extruded polystyrene boards were then utilized to develop microstructure-based finite element models based on the socalled idealized realistic Kelvin cell. The finite element simulation was accomplished with the help of the nanoindentation technology to explore the mechanical properties of the cell wall material. The finite element models were validated by comparisons between the simulated and the experimental results. It has been found that the mechanical properties of the foam in different loading directions can be adequately simulated using the approach of the idealized realistic Kelvin cell. With the help of these models, a parameter study was carried out. This study included the effect of cell size and cell anisotropy on the mechanical response of extruded polystyrene boards under compression stresses. Charts relating between the foam microstructure characteristics and the compression behavior were generated based on the parametric study.