The classic Kachanov–Rabotnov (KR) creep damage model is a popular model for the design against failure due to creep deformation. However, the KR model is a local approach that can exhibit numerically unstable damage with mesh refinement. These problems have led to modified critical damage parameters and alternative constitutive models. In this study, an alternative sine hyperbolic (Sinh) creep damage model is shown to (i) predict unity damage irrespective of stress and temperature conditions such that life prediction and creep cracking are easy to perform; (ii) develop a continuous and well-distributed damage field in the presence of stress concentrations; and (iii) is less stress-sensitive, is less mesh-dependent, and exhibits better convergence than the KR model. The limitations of the KR model are discussed in detail. The KR and Sinh models are calibrated to three isotherms of 304 stainless steel creep test data. Mathematical exercises, smooth specimen simulations, and crack growth simulations are performed to produce a quantitative comparison of the numerical performance of the models.