This work presents the concepts of limit analysis of structures which are constituted by Elastic perfectly plastic material, aiming at the calculus of collapse load in plane frames. The kinematic, equilibrium, and constitutive equations have been established with the use of generalized variables. In order to define the conditions of plastic admissbility, we have considered the option of limit surfaces depending exclusively on bending moments, or else taking account of interaction between bending moments and axial forces. Equations defining the limit surface of I rectangular sections, circular, and hollow sections, and sandwich beams, have been developed. The phenomenon of plastic collpse has been mathematically characterized, and identified as an optimization problem, through consideration of the static and kinematic theorems of proportional limit load, which have been enunciated respecttively as principles of maximum and minimum. Since the limit analysis is an optimization problem, the solution methods utilized are those of mathematic programming theory specially that of linear programming, and the abalysis of the results shall take into account the fundaments of this mathematic theory. As application models, the work presents examples of plane frames, arches, and trusses.