Static compression and splitting tests were carried out for four kinds of EPS (expanded polystyrene) concrete, the stress strain relationship model of EPS concrete with lower (apparent) density was established, in which the physical meanings of parameters were given. The results show that EPS concrete with higher density has remarkable characteristics of quasi brittle materials, whereas EPS concrete with lower density has remarkable characteristics of bubble energy absorption materials. The stress strain relationship model of EPS concrete with lower density agrees well with the experimental results. The particle size effect on relative splitting strength is obvious for EPS concrete with same relative density. The particle size effect on relative splitting strength for EPS concrete reduces with decreasing relative density.