Creep deformation and rupture experiments are conducted on samples of the Ni-base superalloy directionally solidified GTD-111 tested at temperatures between and 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.