This paper provides a short survey of some recent advances in the mathemati
cal modelling of materials behaviour under creep conditions. The tertiary c
reep phase is accompanied by the formation of microscopic cracks on the gra
in boundaries in such a way so that damage accumulation occurs. The paper i
s divided into three parts. Firstly, the damage state in a uniaxial tension
specimen is discussed and the time to rupture calculated. The second part
is concerned with the creep behaviour of materials in multiaxial stress. Be
cause of its microscopic nature, damage generally has an anisotropic charac
ter even if the material was originally isotropic. The fissure's orientatio
n and length cause anisotropic macroscopic behaviour. Therefore, damage in
an isotropic or anisotropic material, which is in a state of multiaxial str
ess, can only be described in a tensorial form. Thus, tensorial constitutiv
e and evolution equations have been developed. Some examples for practical
use are discussed. Finally, some own experiments are mentioned which have b
een carried out in order to validate the mathematical modelling.