ABSTRACT This work intends to present the development of a formulation based on Continuum Damage Mechanics to deal with elastic media introducing different mechanical behaviors in tension and compression regimes as well as some anisotropy degree when damage processes take place. First of all, a formulation for bimodular and anisotropic elastic media is reviewed. To take into account the damage processes in the material, some improvements are proposed as well as the definition of a hyperplane in order to divide the strain space to deal with bimodular materials. Besides, fourth-order anisotropic tensors are requested by the formulation depending on the class of anisotropy. Soon after, two models of constitutive damage written accordingly with the formulation proposed in this work are described. Finally, it is shown that the proposed formulation is an easy way to write and to understand complex constitutive damage models.