This work dissertation presents the implementation of numerical limit analysis with mixed-weak formulation, based on the the lower bound limit theorem and its application in axisymmetric stability problems. The finite element formulation was implemented in Matlab, where the optimization problem is established, which comprises the definition of the equilibrium equation and the adaptation of the Drucker-Prager and Mohr-Coulomb rupture criteria to the second-order cone programming and semidefined programming, respectively, and which is later solved with the Mosek Aps 9.2 algorithm. As a result of the optimization problem, the collapse factor and the speed field can be obtained, allowing to identify the rupture mechanism.The present work focuses on the stability analysis of a well that is carried out in 3 phases, depending on the conditions considered in the model. The results obtained in the axissymmetric analysis were validated through analysis in three-dimensional models and compared with results of plaxis 2D and Optum G2 software, also included the results of MPM modeling, with the software MPM-PUCRio. Finally, the case of the load capacity of a shallow circular foundation is studied, the results of which are compared with those presented by other authors.