Injection and production of fluids into/from the subsurface has been known to trigger earthquakes, referred to as induced seismicity. This seismicity may occur when anthropogenically caused changes in the in-situ stress conditions result in reactivation of pre-existing faults in the subsurface causing slip accompanied by sudden release of energy. Several studies have numerically modelled the induced stresses due to production/injection in reservoirs of various geometries. In this report we present a simplified three-dimensional reservoir with a displaced fault and derive analytical expressions for induced stresses in and outside the reservoir due to production and injection of fluids. We use the calculated stresses for the three-dimensional model and analyse onset of slip across the fault. The research builds upon the analytical two-dimensional plane-strain analysis for induced stresses and slip initiation in \citet{Jansen2019} to which our work contributed. We reaffirm the findings from the plane-strain analysis in \citet{Jansen2019} and conclude that the effects of incorporating third dimension on induced stresses and slip behaviour are limited. We find infinite peaks in resultant shear stresses at the reservoir boundaries and observe a distinctly different pattern in induced stresses and slip behaviour between production and injection scenarios. In case of production, the slip patches are predicted to grow inwards into the reservoir initially until they merge, while for injection the slip patches grow separately into the overburden and underburden. The findings in this report are in agreement with the previous analytical and numerical studies on induced seismicity. In this research we also introduce geometrical complexity in the reservoir in the form of laterally varying height of the reservoir and we observe that the effects of variation in reservoir thickness are also minimal, however the induced stress patterns and slip initiation is significantly impacted by fault throw, initial stress conditions and fault frictional characteristics.