A modification of Grьneisen’s equation of state describing an analytical relation between the Hugoniot states and other thermodynamic states for carbon fiber-epoxy composites with micro- and macro- fractures under shock wave loading is proposed. Using nonlinear anisotropic constitutive equations for damageable solids and generalized decomposition of a stress tensor, the three-wave structure of shock waves, consisting of nonlinear anisotropic, transition (failure-wave) and isotropic elastic parts, is examined in different directions for selected carbon fiber-epoxy composite. A numerical calculation shows that Hugoniot stress levels well agreed with the experimental data for selected carbon fiber-epoxy composite.