The present work proposes a computationally efficient stochastic statistical method (called Green-FOSM) that considers uncertainties in geomechanical problems, with the objective of improving the decision-making process related to problems associated with the process of fluid injection or depletion. The novelty of the method lies in the use of the Green s function approach (GFA), which, together, with the first-order second-moment statistical method (FOSM), is used to propagate uncertainties associated with the mechanical properties of material to the displacement field of the geological formation. Furthermore, using the concepts of stochastic grid and autocorrelation function, the proposed method allows the consideration of the spatial variability of random variables that represent these mechanical properties. The GFA uses the fundamental solutions of classical mechanics (Kelvin fundamental solution, Melan fundamental solution, among others) and the reciprocity theorem to calculate the displacement field of a geological formation with irregular geometry, and different types of materials. The great advantage of this method compared to the classical finite element method (FEM) is that it does not require the imposition of boundary conditions and the analysis of the problem can be performed considering only the reservoir or other regions of interest. This modeling strategy decreases the degrees of freedom of the model and the CPU time of the deterministic analysis. In this way, as the GFA requires less computational effort, this approach becomes ideal for propagating the uncertainties in geomechanical problems. Initially, an iterative version of the Green-FOSM method was proposed, which presents statistical results similar to those found through the classic Monte Carlo simulation (MCS). In this initial version, the displacement field is calculated using an iterative numerical scheme, which decreases the computational performance of the method and can generate convergence problems. Such limitations would restrict the application of the PUC-Rio - Certificação Digital number 1912634/CA original GFA and the iterative Green-FOSM method in real problems. Thus, the present work also developed a new version of the GFA, which uses a non-iterative numerical scheme. For the proposed validation problems, the non-iterative method proved to be up to 17.5 times faster than the original version. This version is able to expand the applicability of the GFA, since the convergence problems were eliminated and the results obtained by this method, when analyzing a representative geological profile of the Brazilian pre-salt, are similar to those found via FEM. Finally, based on the non-iterative GFA, a non-iterative version of the Green-FOSM method was proposed. This non-iterative version is capable of probabilistically analyzing complex geological formations, such as the Brazilian pre-salt geological formations. Using the same computational resources, the non-iterative GreenFOSM method is at least 200 times faster than the iterative Green-FOSM method. In general, the results found in the investigated analyzes (deterministic and probabilistic) are close to the results obtained by the reference method (FEM and MCS, respectively).