Abstract: In order to establish the constitutive model of solid composite propellants with damage, at a mesoscopic scale, the damage of the material was considered in a micro-cracking form, and the crack density was chosen as internal damage variable. On the basis of Abdel-Tawab's constitutive equation, the damage mapping tensor which was derived in a general form by using the homogeneous theory of microcracks. Usually, the damage mapping tensor is minor symmetric, and its physical significance is that mapping a multiaxial loading on an anisotropic material in true stress space into a more complicated multiaxial loading on an isotropic material in effective stress space. Secondly, a damage evolution equation was obtained based on the dynamic model of crack growth in viscoelastic material and the concept of crack growth resistance curves. There are only four micro-parameters which have clear physical meanings and similar variation tendencies with macro-stress curves in damage evolution equation. Numerical results indicate that the model can correctly reflect the anisotropic damage feature of material, the dependence of damage on strain rate and temperature, and the capacity to predict creep damage behavior reasonably.