Unified descriptions of the constitutive and evolution equations of elastic-brittle-damage materials are developed on the basis of irreversible thermodynamic theory for constitutive equations. The Helmholtz free energy is assumed to be a function of modified elastic strain εe and second-rank symmetric damage tensor D by taking account of the effects of crack closure and damage anisotropy, and a damage dissipation potential related to the entropy production rate is expressed in terms of damage-conjugate force Y. The constitutive equation and the damage evolution equation derived by these potentials were applied to an elastic-brittle-damage material. The anisotropic elastic-brittle-damage behavior of high-strength concrete under uniaxial, proportional and non-proportional combined loading was analyzed to elucidate the utility and the limitations of the present theory.