In the pressure vessel and piping and power industries, creep deformation has continued to be an important design consideration. Directionally solidified components have become commonplace. Creep deformation and damage is a common source of component failure. A considerable effort has gone into the study and development of constitutive models to account for such behavior. Creep deformation can be separated into three distinct regimes: primary, secondary, and tertiary. Most creep damage constitutive models are designed to model only one or two of these regimes. In this paper, a multistage creep damage constitutive model is developed and designed to model all three regimes of creep for isotropic materials. A rupture and critical damage prediction method follows. This constitutive model is then extended for transversely isotropic materials. In all cases, the influence of creep damage on general elasticity (elastic damage) is included. Methods to determine material constants from experimental data are detailed. Finally, the isotropic material model is exercised on tough pitch copper tube and the anisotropic model on a Ni-based superalloy.