The principle for the design of a directional drainage borehole in a foliated formation is such that the borehole is drilled so that it crosses all the interested foliation planes. If the inclination angle of the borehole is not appropriately selected, the borehole might never reach the concerned foliation planes. In other words, there exists a critical inclination angle for the borehole. The borehole is able to cross the concerned foliation planes only at an inclination angle larger than the critical angle. The critical inclination angle depends on the geological structure of the foliation planes as well as the trend of the drift. The method to determine the critical inclination angle is described both graphically and analytically in this paper. A case for design of drainage boreholes in a copper mine, using the developed method, is also presented