Mechanisms that are associated with acceleration of the creep rate in the tertiary stage such as microstructure degradation, cavitation, necking instability and recovery have been known for a long time. Numerous empirical models for tertiary creep exist in the literature, not least to describe the development of creep damage, which is vital for understanding creep rupture. Unfortunately, these models almost invariably involve parameters that are not accurately known and have to be fitted to experimental data. Basic models that take all the relevant mechanisms into account which makes them predictive have been missing. Only recently, quantitative basic models have been developed for the recovery of the dislocation structure during tertiary creep and for the formation and growth of creep cavities. These models are employed in the present paper to compute the creep strain versus time curves for copper including tertiary creep without the use of any adjustable parameters. A satisfactory representation of observed tertiary creep has been achieved. In addition, the role of necking is analysed with both uniaxial and multiaxial methods.