INTRODUCTIONThe aim of the present exposition is to summarize the main algebraic properties of classical plasticity, and thus help the understanding of the mathematical context of shakedown studies. Hence nothing new must be expected, except some few improvements concerning presentation and hypothesis enlargement; for instance the new concept of "elastic sanctuary" has recently been introduced by the author and D. Weichert [1993] in order to give a maximal extension to the assumptions which ensure the classical proofs. We shall stay within the linear framework generated by the hypothesis that displacements and strains remain small in the vicinity of some strained configuration. It is well known that such a theory was in a first state of achievement in a famous paper by KOlTER [1964], completed by CERADINI in the dynamic case [1969]. The great progress of the seventies consisted of the first existence theorems in elastoplasticity, by J. J. MOREAU [1973], JOHNSON [1976], SUQUET [1979] and STRANG [1978]. Besides, some other improvements in the shakedown theory were proposed, for instance by KONIG [1987] or DEBORDES and NAYROLES [1976]. This last paper exposed the theory for a body with a finite number of degrees of freedom, together with the new theory of "shakedown domains" mainly devoted to the structural decomposition techniques. Later on O. DEBORDES [1981] established that static and kinematical shakedown formulations effectively define dual problems. No functional analysis framework will be chosen here, for two good reasons: first, we wish to give a general exposition of the algebraical basis of the theory, independently of any particular kind of structure. This structure may be composed of different pieces, with different modelizations : beams, shells, 3D continuum etc. If some functional analysis results exist for this last piece, with the space BD(Q) introduced by SUQUET [1979] and STRANG [1978], almost everything remains to be done for other sorts of solids. The second reason is that, even in the case of a 3D continuum, any exposition of functional analysis would need a full article; reader interested in such questions should read SUQUET [1988].A basic framework of structural mechanics is constituted by the duality between displacements and loads on the one hand, and strains and stresses on the other. As usual in structural mechanics all these terms are understood in a generalized sense. For instance, a displacement may be the deflection of a beam, the rotation of the normal to a shell etc. ; associated loads are defined as the generalized forces associated with these generalized displacements, i.e. by their virtual work (or "virtual power", if preferred...). Generalized displacements, loads, strains and stresses are also understood as fields defmed on the material finite domain Q of IRP occupied by the structure in its reference geometry). At the generic point M of the material domain Q these fields take values which may be called "local displacement", "local strain", etc. In the finite dimensional cas...