This chapter deals with the simulation of the creep process and the effect of long-term strength of metals, notably, in both uniaxial and complex stress states. A description of a creep experiment and the simplest creep models are presented, that is, the theory of steady creep, the theory of ageing, the theory of flow and the theory of hardening. In creep process simulation, a kinetic theory based on the introduction of structural parameters characterising the state of the metal at a given time is widely used. Among such parameters, metal damage in the creep process, work of stresses on creep deformations (energy version) and concentration of an aggressive medium in the metal were studied. The coupled problem of creep and long tensile strength is also considered taking into account the mutual influence of damage accumulation and one-dimensional diffusion of the aggressive medium. The times to fracture are determined both in the presence of an aggressive medium and in the absence of one. A significant contribution of Soviet (Russian), European, American and Japanese scientists to the development of continuum damage mechanics is highlighted.