The effect of creep-fatigue conditions on structural components is not completely understood, and so the prediction of the behaviour and lifetime of such components is often unreliable and inaccurate. One of the methods proposed to improve the predictions is continuum damage mechanics, which provides a general description of material behaviour under degrading conditions. An estimate of life is usually based on the initial behaviour of a component. However, the work of previous researchers has shown that accurate predictions of the creep life of structures require that the stress redistribution due to the growth of damage is taken into account. In this thesis, this work is extended to fatigue and the effect of fatigue damage on life and deformation is studied for multibar model structures. The non-linear kinematic hardening rule is introduced as a constitutive law for cyclic plasticity that models many aspects of the cyclic behaviour of metals. Its properties are studied and it is extended to include the effects of damage on cyclic deformation. Creep-fatigue is studied by combining the models for fatigue and creep. Using published material data, the creep-fatigue behaviour of a two bar structure is studied and the results are compared with some experimental results. A study is made of finite element methods for solving problems involving plasticity and an example problem is solved. A model for the multiaxial behaviour of damaged material is proposed and examined for simple cases. The studies show that stress redistribution has a significant effect on fatigue life and the qualitative properties of the uniaxial models are very close to experimental observations. However, a lack of suitable and consistent experimental data on material behaviour means that the lifetime predictions and the multiaxial models are of uncertain accuracy.