The occurrence of oil and gas well drilling events is common, but undesirable, once it increases time and cost of operations. Its occurence can lead to loss of fluid circulation, wellbore wall collapse, restriction of its functionality, platform damage, environmental issues and even the lost of human lives. stresses knowledge is essential to wellbore stability estimation and to the improvement of drilling safety. In fact, there are some methods and tests to compute the minimum horizontal stress, but there still exist difficulties on maximum horizontal stress determination. In the case of deviated wells, the calculations are even more complexes due to the lack of alignment between the regional stresses and well axis. Identified that problem, and considering that at least one wellbore has been drilled in a field and presented compressive or tensile instabilities, this dissertation works on the implementation of algorithms capable of obtaining the maximum horizontal stress magnitude that lead the appearance of breakout or induced fracture. The instability problems are identified and previously interpreted through image logs. The implemented algorithms involve an analytical solution, which is calculated by an explicit method and an implicit one, to the stated problem. The procedure to the stresses rotation on deviated wells used at this work is based on the formulation presented on technical literature, and the calculation of the stresses around the wellbore wall, on Kirsch s equation. The failure of the material is evaluated using a tensile cutoff for induced fractures and Mohr-Coulomb or Lade-Ewy criteria for breakouts. The developed methods are compared between each other, presenting the advantages and disadvantages of then. The results, applying a large variation on the wellbore inclination and azimuth, show that the values accomplished a low difference in relation to the obtained by using a commercial software, being considered as satisfactory.