The production and injection of fluids from and in reservoirs leads to changes in the in-situ stress in the subsurface. This can cause reservoir compaction, subsidence, fault reactivation and / or seismicity. As these effects may greatly influence society it is of importance to find accurate methods to describe them so they can be predicted or even better, mitigated. This thesis discusses a new analytical approach to calculate stress in the subsurface which incorporates the effects of differential compaction on the initiation of fault reactivation. This new approach is named Differential Compaction Loading (DCL) and the reason for its development is due to discrepancies observed between calculations using the Mohr-Coulomb failure criterion, also known as Poro-elastic Loading (PEL), and field observations. Geomechanical modelling was performed to assess fault failure sensitivity to a range of geometrical aspects as well as reservoir and fault properties. From this analysis, focusing on the reactivation pressure at which failure first occurs, an empirical sense of sensitivity was established. It was found that for the examined variations in the geometry the fault dip angle resulted in the largest spread in reactivation pressure. For the examined reservoir and fault properties, the friction angle was found to have the largest sensitivity. With these results it was possible to improve the estimates of essential parameters within the analytical approach, yielding a better fit between analytical and modelled solutions. These solutions lie closer to field observations. Hence, the new method of DCL shows a great improvement in calculation of stresses in the subsurface, compared to the method of PEL. This calibrated analytical approach allows for a quick assessment of the fault stability within a reservoir. Additionally, through the results from the geomechanical model new insights were obtained into the way stresses change and behave when a reservoir is depleted. The rotation of the principal stresses for each level of depletion was quantified and a new definition of the critical fault angle, the dip angle which will fail first, was derived. This links the depletion pressure and related rotation angle directly to a value of the new critical fault angle when DCL is present. Ultimately, these new insights into fault failure behaviour of boundary faults could be a useful tool in the step towards prediction and mitigation of production or injection related seismicity.