In this paper we report a technique for estimating the Partial Discharge (PD) inception voltages in case of discharges occurring at the interface as well as in voids in the ambient medium of Sulphur Hexafluoride gas (SF 6 ). Since occurrence of PD is a phenomenon dependent on upon many factors such as the type of gas in the void, the gas pressure, surface properties of the void, size and shape of the void, dielectric constant of the surrounding medium; these parameters have to be taken into account. The computed values are valid in the pressure range of 0.067 kPa to 101.333 kPa. Computations are accurate to ± 3.5 % in the pt′ range of 0.3 -1200 kPa-cm. These computations are useful in understanding discharges in the insulation system of cables, capacitors, GIS, bushings or epoxy cast equipment which are dried and impregnated at low pressures and may contain gas pockets at sub-atmospheric pressures. These computations are also important and useful for high altitude insulation design and spacecraft insulation.