Wellbore stability problems are known to cost the oil and gas industry billions of dollars each year. However, these costs can be significantly reduced through the application of comprehensive geomechanical models. The first objective of this book is the comparison of several failure criteria, named the Mohr-Coulomb, Mogi-Coulomb, Modified Lade and Tresca yield criterion and to apply them in order to determine the optimum drilling direction and mud pressure. The results showed that the Mohr–Coulomb and Tresca criteria estimate the highest minimum mud pressure and mud density required for wellbore stability while the Mogi-Coulomb and the Modified Lade criteria estimate the lowest minimum mud pressure and mud density. The second objective is application of finite difference method to estimate the mud pressure required to avoid borehole collapse for a well located in Iran oil field. Moreover, it is aimed to monitor the changes around wellbore during production and with a view to optimizing well planning, construction and post evaluation procedures.