This thesis presents the analysis of the stresses and strains in elastic-plastic structures, using a mathematical programming approach and some solution techniques for this problem. The evolution of the stresses and strains occuring in one elastic-plastic structure, loaded by a time varying load, is defined by a system of equations and inequations obtained from the constitutive relations of the material and from the compatility and equilibrium conditions of the structure, expressed in terms of rates. This system is equivalent to the Kuhn-Tucker conditions needed for the minimization of a quadraditic funtional with equality and inequality constraints. An incremental formulation for the elastic-plastic problem is adoted to solve this optimization problem by numerical techniques, enabling the determination of stresses and strains evolution in the structure due to finite load increments.