Wellbore instability issues represented by well collapsing resulted in a tremendous loss of time and money in the oil industry. This leads to the need of more critical well drilling plans to prevent such rock failure. The carbonate rocks are known to be more competent and experience less instability issues than shale or sandstone. However, the majority of the global hydrocarbons reservoirs are carbonate. Consequently, a significant number of wells are drilled every year in carbonate formations. This has raised the amount of wellbore instability issues encountered while drilling carbonate formations worldwide. Rock failure will take place when the rock mass in the field experiences a huge stress beyond its strength. Building models that can predict the circumstances under which a rock might fail, would massively help in preventing severe issues such as borehole collapsing and solids production. Hence, the most appropriate mud density and borehole trajectory should be known in advance before drilling through proper geomechanical modeling. In this thesis, a linear elastic model for the stresses in the field is used together with the Mogi Coulomb failure criterion as a geomechanical stability model. This three dimensional stability model reflects and represents the impact of all existing principal stresses in the fields. The stability model is used to generate a several charts to be available and accessible for all drilling engineers and operators in Oman. For carbonate rocks, the stability charts provide the minimum allowable mud density to prevent borehole collapse for all borehole trajectories. The developed charts are specified for some ranges of rock geomechanical parameters due to the focus on the carbonate formations of Oman and the most encountered options. The developed stability charts are categorized according to the input parameters. The effect of each geomechanical property is studied to understand the relationships among them. Real field case studies are conducted utilizing the developed charts for carbonate formations in Oman and outside the country. The applied mud density and the associated drilling trajectory in the studied fields was consistent with the predicted results from the developed charts. These results encourage the usage of the stability charts to simplify the analysis and reduce the borehole instability issues represented by borehole collapse in carbonate formations.