Drilling non-vertical wells, which is commonly used to enhance production, in particular in unconventional reservoirs with very low permeability, is subjected to rock mechanics related issues namely wellbore instabilities. Drilling in the same formation but with different deviations and at different directions would not result in similar response in terms of rock failures. This is due to the rotation of the induced stresses around the wellbore wall along its trajectory. The type of instabilities that the formation experiences around the wellbore is a function of formation’s mechanical properties and the status of in-situ stresses. It is clear that none of these natural parameters can be controlled or changed during drilling operation. However, the density of the mud weigh which is used to drill the wellbore could be optimised in order to mitigate or stop wellbore instability issues in the form of tensile failure or fracturing in case of using high mud density or shear failure or breakouts when a low mud weigh is used. Therefore, a safe mud weight window (MWW) can be determined for optimum drilling in terms of having the least issues related to wellbore instabilities. This MWW will change as the wellbore deviation changes. In this paper, the concept of constructing the rock mechanical model (RMM) which includes the rock mechanical properties as well as in-situ stress profiles is briefly presented. Then the RMM output corresponding to vertical well Arrowsmith-1 which is a shale gas well drilled in the North Perth Basin of Australia will be used to calculate the safe MWW for drilling wellbores in different azimuth and deviation in the field. The results indicate how the MWW changes as a function of wellbore trajectory.