According to estimates from the Schlumberger Market Analysis 2007, 60 % of fossil conventional hydrocarbons worldwide are located in naturally fractured reservoirs (NFR). In these reservoirs large volumes of hydrocarbons have been left untouched. Gas-oil gravity drainage (GOGD) is a well-known production method that leads to high recoveries, while also being relatively inexpensive as compared to other production methods. It can occur naturally during gas cap expansion or when gas is actively injected at top of the reservoir. Gravitational forces then lead to a downward displacement of the oil, where both gas and oil are present. Although this process has been thoroughly examined for conventional reservoirs and in naturally fractured reservoirs using dual continuum approaches, very few publications exist on gravity drainage of NFR as simulated using discrete fracture and matrix approaches (DFM). This remains an active field of research explored by this thesis. My primary goal is to perform sensitivity analyses on the critical balance between capillary and gravity forces in NFR undergoing GOGD and to determine when gravity drainage is a feasible and recommended process. These questions are addressed with the help of a proprietary reservoir simulator based on finite difference method. Three simplified models with a single vertical fracture and one more realistic layered discrete fracture and matrix model, based on field observations from Door County, Wisconsin, USA, were used as input to my simulations. The conclusions reached are that single vertical fractures do not significantly affect the homogeneous models. Although the fracture helps draining the near-fracture region, the rock further away is left unaffected. Flow is mainly vertical and could be approximated by a piston-like displacement. This, however, is not the case in the more realistic model with layers. Here the fractures have a significant effect on the drainage speed and their presence increases recovery as compared with an unfractured model. The gas preferentially flows through the fractures and thereby by-passes horizontal low-permeable layers entering higher-permeable layers, where GOGD is initiated. The results also indicate that GOGD is strongly influenced by boundary conditions .The sensitivity analysis also confirms the importance of well established critical factors like fluid density contrast, oil viscosity, relative permeability and capillary pressure. The thesis reaffirms the high production potential of gas-oil gravity drainage for NFR.