Abstarct: The economy of the oil-rich countries is almost affected by petroleum production rate. Hence, scientists and researchers have focused on removing the interruptions and making the production precess as continuous as possible. Simultateous drilling instabilities are one of those obstacles which make unwanted delays in petroleum production. In addition, repairing a collapsed well in not only a time-consuming process, but also it is costly. As results, it seems to be essentional to determine the geomechanical parameters affecting the wellbore stability. Wellbore stability could be separated into drilling problems and reservoir depletion induced problems. Wellbore instability factors could be known as controllable and in incontrollable branches as well. Drilling induced problems are mostly controllable factors affecting the wellbore stability. On the other hand, tectonic condition, stress distribution and rock mechanical parameters could be placed in incontrollable or imposed parameters branch. This is while; a comprehensive understanding of geomechanical condition of the field can diminish the instabilities considerably. In this thesis, firstly, the geomechanical parameters affecting the wellbore stability are determined; Secondly, Mechanical Earth Model is introduced and applied as a solution to predict mud weight window (MWW) using rock failure criteria; Thirdly, a numerical solution is applied and the results are validated; And finally, sensitivity analysis for parameters affecting the wellbore stability is done. The results show that 3 dimensional failure criteria will predict more realistic response for MWW rather than other linear and non-linear 2 dimensional criteria. Moreover, elastic modulus, pore pressure and mud pressure have the most effect on wellbore stability. This is while parameters such as internal friction angle and cohesion will affect the failure geometery.