Numerical limit analysis was studied in order to evaluate an effective numerical procedure to solve three-dimensional slope stability problems. This numerical approach utilizes finite element method and mathematical programming. Mathematical programming is needed because the plasticity theorems, basic theorems for limit analysis, can be cast as optimization problems. The lower bound theorem consists of finding the maximum collapse multiplier that will lead the soil to the imminence of collapse. The soil will still be restricted to equilibrium conditions and the yield criterion will have to be satisfied everywhere. Drucker- Prager was the yield criterion chosen. In this thesis, the optimization problem is reformulated as a second order cone programming (SOCP). SOCP is known to solve large-scale problems with great computational efficiency and we used the solver Mosek. The model calculates not only the collapse multiplier, but also the safety factor for the slope. A strength reduction scheme was proposed, based on the Newton-Raphson method. For complex geometries cases, a novel formulation was developed. A fictitious horizontal force was added at the equilibrium equation and uniquely this force was increased by the multiplier factor. It was only through this reformulation that it was possible to assess stability of slopes subjected to porepressure effects. The groundwater flow was simulated separately in a finite element program developed by Miqueletto (2007). The soil strength depends on porepressure values, which define soils as saturated or unsaturated.