The study on wellbore stability has as one of its main application the determination of the safe range of the drilling-fluid density. The wellbore stability analysis is controlled by a number of parameters that generally present uncertainties associated to their values. In conventional methods, these uncertainties are not considered. The purpose of this work is to develop methodologies of analysis of wellbore stability that consider the uncertainties associated to the controlling parameters. Methods for quantifying the uncertainties associated to the parameters are presented for the case of an open well and for the case of new well located on a development region. Two methods of sensitivity analysis are also presented and applied to the well stability problem. To evaluate the effect that the uncertainties associated to the parameters create on the stability analysis, two probabilistic methods were applied to the problem, and compared to each other. Based upon Monte Carlo method, a computational simulator was developed in order to carry out probabilistic analysis of wellbore stability. The simulator takes into account the uncertainties associated to the parameters. The probabilistic methods of analysis, presented in this dissertation, provide the probability of failure associated to the different internal pressure of the well. As these pressures are dependent upon the density of the drilling - fluid, the evaluation of the risk associated to these pressures constitutes a new criterion to establish the density of the drilling -fluid.