Regeneratively cooled nozzle structures belong to the critical components of a space shuttle main engine. The cooling channel wall in the combustion chamber is subjected to extreme cyclic thermomechanical loadings which eventually lead to the damage of the wall, well known as the ”dog-house” effect. A material model for the purpose of reliable lifetime prediction is being developed. The model shall describe the material behaviour under hardening conditions as well as the superimposed effect of fatigue which occurs due to cyclic loadings. Motivated by extending the classical rheological model for elastoplasticity with Armstrong- Frederick kinematic hardening, a viscoplastic model is formulated in the small strain regime. The coupling with damage is performed using the well-known concept of effective stress and the principle of strain equivalence. Parameter identification on the basis of experimental results for the high temperature copper alloy NARloy-Z, which is one of the typical cooling channel liner materials, is performed. The applicability of the model will be shown by means of sequentially coupled thermomechanical analyses.