Creep deformation and rupture experiments are conducted on samples of the Ni-base superalloy directionally solidified GTD-111 tested at temperatures between 649°C and 982°C and two orientations (longitudinally and transversely oriented). The secondary creep constants are analytically determined from creep deformation experiments. The classical Kachanov–Rabotnov model for tertiary creep damage is implemented in a general-purpose finite element analysis (FEA) software. The simulated annealing optimization routine is utilized in conjunction with the FEA implementation to determine the creep damage constants. A comparison of FEA and creep deformation data demonstrates high accuracy. Using regression analysis, the creep constants are characterized for temperature dependence. A rupture prediction model derived from creep damage evolution is compared with rupture experiments.