Abstract: A general theory for hygrothermal elastic anisotropic damaged composites was developed on the theoretical basis of irreversible thermodynamics without any hypothesis. The constitutive functional expansion method was used for damage constitutive equation. All of the general representations of constitutive equations for hygrothermal elastic damaged materials were derived. These constitutive equations included specific free energy density expression, stress-strain relation, entropy density equation, damage strain energy release rate expression, hygroscopic dual force expression, hygro-thermo-stress-damage coupled heat conduction equation and damage evolution equations. The results show that there are several damage effect functions in constitutive equations, which indicate the influences of damage on the macroscopic mechanics properties and hygrothermal properties of materials. The detailed expressions of the damage effect functions could be determined by micromechanics, which relate the continuum damage mechanics with the microscopic damage mechanics. Finally, the determination methods of damage effect functions and coefficient tensors were illustrated from two aspects of micromechanics and experimental observations, which provided important theory basis for analyzing damage problems of composites under the variable temperature and humidity circumstances.