The elastic-plastic analysis of structural components is considered. The formulation of the constitutive equations is specially focused. The constitutive relation for rates is derived from pseudo-potentials by using the sub-gradient concept. Internal variables are introduced to describe dissipation mechanisms and thermodynamical concepts are used in order, to obtain the corresponding potential relationships. Generalized potentials are also presented for the approximate constitutive relation in terms of finite increments of strain and stress. This formulation incorporate plastic admissibility constraínts and it is also able to describe local elastic unloading except the case when it follows plastic yielding in the true incremental process. This form of the constitutive equation is used next to obtain minimum principles for the elastic-plastic analysis. Spatial discretization is performed by means of the Finíte Element Method. Some algorithms are discussed for the solution of the variational formulations considered. Numerical applications are presented for plane problems and plate bending.