Modelling of elastic anisotropy induced by creep damage and its application to the analysis of creep crack growth in a copper plate are discussed. The elasticity theory of damaged materials developed by M. Kachanov is combined with the anisotropic creep damage theory of the present authors to formulate the anisotropic elastic-damage coupling in creep. The theory is implemented into the finite element analysis of the creep damage process in a thin plate with an internal crack subject to non-proportional loading. The material constants of elastic-damage coupling were identified by performing an experiment. The influence of the reduction in elastic modulus due to creep damage on the stress distribution at the crack tip, on the pattern of creep crack extension and on the final rupture time are discussed in detail.