|This paper presents revised and extended version of theory proposed in the late 1970-ties by A.
·Cyras and his co-workers. This
theory, based upon the notion of duality in mathematical programming, allows us to generate variational principles and to investigate existence
and uniqueness of solutions for the broad class of problems of elasticity and plasticity. The paper covers analysis of solids made of linear elastic,
elastic-strain hardening, elastic-perfectly plastic and rigid-perfectly plastic material. The novelty with respect to
·Cyras’s theory lies in taking
into account loads dispersed over the volume and displacements enforced on the part of surface. A new interpretation of optimum load for
a rigid-perfectly plastic body is also given.