An 'incremental form' of anisotropic damage constitutive equation is proposed both for brittle and ductile materials. Based on the concept of irreversible thermodynamics that damage processes are history independent coupled with irreversible energy dissipation, two types of definition for damage representation are established, known as damage tensor D and damage strain tensor nd, to describe constitutive responses of damaged materials. A state variable coupled with damage and other observable state variables, i.e. ha, is formulated separately from other internal variables and defined as an equivalent damage variable. A constitutive relation due to damage is finally formulated by introducing 'damage flow potential function' employing the theory of irreducible integrity bases. A clear physical representation based on theoretical foundations and rigorous mathematical arguments of the conventional damage models defined in terms of 'damage effect tensor M(D)' is also elucidated. Validity of the proposed model is verified by comparing with the formulations of conventional damage effect tensor. A plastic potential function coupled with damage is also introduced by employing the anisotropic plastic flow theory, so that the proposed damage model can be applied to characterize a wide range of damage problems of practical engineering interest.