The present work has the purpose of studying the behavior of geotechnical structures by means of numerical analysis. For this, program GEOLIMA (GEOtechnical LIMit Analysis) was developed based on the theory of Numerical Limit Analysis using the Finite Element Method (FEM), considering bidimensional and three-dimensional problems. Due to the fact that the properties of the ground are generally random variables, Non Deterministic Analysis was also considered by means of the Linear Statistical and the Monte Carlo Methods. Initially, the fundamentals of Deterministic Limit Analysis and its mixed formulation are presented. Then, the fundamentals of Non Deterministic Theory are presented, and the Linear Statistic and the Monte Carlo Methods are described. The development phases of GEOLIMA are briefly described. Its validation is made by comparing the results obtained with analytical solutions or other solutions. Following, a 2D application is made with the purpose of illustrating Deterministic and Non Deterministic Limit Analysis. Finally, two 3D applications are presented: a problem related to the excavation of a tunnel front and a problem related to mining panels. The results of this work indicate the viability of using Deterministic and Non Deterministic Limit Analysis in the study of geotechnical problems.