In this study, the constitutive equation for the materials including voids is proposed. Anisotropy and compressibility caused by distribution of voids are taken into account. Influence of voids distribution is represented by damage tensor in order to represent anisotropy and compressibility. The constitutive equation is derived by consideration based on thermomechanics. Dissipation inequality and yield function are proposed so that anisotropy is represented. Accuracy of this theory is validated by comparing the theoritical value and the finite element analysis of the model which assumes regularly arrangement of voids. The yield loci predicted by the theory showed good agreement with the curves calculated by FEA.