Fundamental concepts of Solid Mechanics, usually developed in literature with reference to a 3D continuum, are here introduced for a discrete deformable device. It is a 1D object, immersed in a 3D space, whose end-points are polar point-bodies. Kinematics, Statics, Virtual Work, Elasticity, Internal Work and Plasticity are discussed for this element. Strains are defined as the difference between the generic displacement gradient and the rigid displacement gradient. Stresses are defined as equilibrated system of forces that the element exchanges, for contact, with the environment. Duality between congruence and equilibrium, allowing to express the internal virtual work as scalar product between stresses and strains, is commented. A hyper-elastic linear behavior is first assumed. The internal work is defined, with the related potential and complementary energies. Semi-definite elastic devices are analyzed, for which a reduced number of significant strains/stresses exist. Simple devices are considered, i.e., extensional and flexural springs, which, when assembled, constitute more complex multiple devices. Elasto-perfectly plastic devices are then studied. The constitutive law is written using alternatives, both in finite and incremental forms. Important theoretical aspects, as the dissipated energy, the elastic domains, the Principle of Normality, the progressive plasticization and the residual stresses, as well operational tools, as the idealization of plastic hinge with relevant ultimate bending moment, are commented, always referring to simple discrete models.