Coated fuel particles, as used in high-temperature gas-cooled reactors, consist of a fuel kernel and a spherically symmetric multilayer coating. During their lifetime they undergo varying stress states, caused by the simultaneous occurrence of a number of basic physical effects. These effects are discussed on the basis of the presently known data and classified in “actions” and “reactions”: The actions, tending to cause deformations, are fuel swelling, fission gas development, irradiation-induced dimensional changes and thermal expansion; the reactions, tending to restrain the deformations, are elastic and plastic effects, characterized by the build up of stresses. Model calculation of the stress and deformation state in the system is complicated by delayed elastic- and plastic effects, called transient- and steady-state creep, and by the anisotropy and the differential behaviour in and between the materials: UO 2, pyrocarbon, SiC. Model development, which is reviewed here, however allowed one to describe the total “stress history”: it begins with differential thermal expansion during and after fabrication and continues with fast and thermal neutron induced dimensional and density changes, fuel swelling and gas pressure development. It still proceeds when mechanical effects such as decoupling, recoupling and failure of single layers occur as a consequence of critical states of stress and deformation. It does not end before all layers are broken. The concepts of such a highly developed mathematical model are discussed. They are based on a division of the stress history into single consecutive intervals, each one with small enough deformation- and stress variations to allow treatment by the methods of the “classical” linear theory of elasticity. Calculated examples are given, which predict the mentioned physical and mechanical effects. Present practical experience and knowledge of data show, that mathematical model considerations cannot replace test experiments as much as in classical fields. They are important however in designing the experiments and necessary in interpreting them; they provide the only reasonable possibility of extrapolating the results of test irradiations to power reactor conditions.