Abstract: The Eshelby equivalent inclusion method is an effective method to establish the constitutive models for elastoplastic and damage rock.There have been only a few publications addressing the Eshelby equivalent inclusion method for establishment of the constitutive models until now.In this paper,a Helmholtz free energy function for damage rock with plastic volume strain is set up by the Eshelby equivalent inclusion method in the framework of continuum damage mechanics.A constitutive equation for damage rock with plastic volume strain is obtained from the Helmholtz free energy function with the theory of continuum damage mechanics.The corresponding damage evolvement equation and an evolvement equation of plastic volume strain are deduced.Numerical results show that the constitutive model can reflect the plastic volume strain affecting damage and damaged rock can not transfer tensile stress.