This collection of papers is a state of the art presentation of theories and methods related to the problem of the behaviour of mechanical structures under variable loads beyond their elastic limit in particular, the problems of shakedown, ratchetting, transient and asymptotic cyclic states are addressed. the volume is composed of four chapters devoted to material modelling for cyclic loading conditions; general theory of accommodated states of structures; effects of changes of the geometry on the inelastic structural response; and numerical techniques with applications to particular engineering problems. it was aimed to provide a unified approach in order to understand both inelastic material and structural response under variable loading conditions. the attempt to extend the classical shakedown theory of melan and koiter to geometrically non-linear problems is presented in several papers. the industrial application of cyclic plasticity to the analysis and the design of pressure bellows, compensators, turbine disks, or flange connections under thermal and pressure cycles illustrates the great potential of the numerical techniques developed for this purpose using mostly min-max approaches. the treatment of railway problems and the analysis and optimisation of pavements are further examples of important areas of applications. emphasis was laid on approaches that take into account the fact that loading histories are often not precisely known therefore, the center of interest lies in other than step by step calculation methods.