The work begins with a theoretical description of conductivity and the importance of this material property in the electrical power industry. The various theories describing high voltage conduction in highly insulating dielectric liquids are analysed to ascertain their propensity to explain the exponential rise in the conductivity of the insulating liquid at high fields.The work goes further to analyse the various methods and standards that are presently utilised in the measurement of conductivity of highly insulating oils. The short-comings of the present methods particularly the IEC 61620 and 60247 are identified. The physics behind the peculiar behaviour of the conductivity when stressed under high electric fields is described and analysed.Measurements carries out according to a standard, may not lead to useful results. Therefore, it is preferable to determine the conductivity under practical aspects and also to measure the different parameters on which the conductivity depends (1). A new method of carrying out conductivity measurements based on the use of triangular and sinusoidal input high voltage is used in this work.Conductivity analysis is carried out based on this method while time dependency, frequency dependency and field dependencies are studied.The results of the various results show a strong dependency of the resistance of the oil on the input electric field up to two powers of ten; when the electric field is varied from zero to 10 kV/mm for all frequencies. The frequency of input voltage has a minimum effect of the results of the conductivity up to 0.1 Hz; the only observable change is the increasing values of the capacitive current component of the measured total current.The time dependency of the resistance values shows a very remarkable variation of conductivity. There is an average of 3 times in the conductivity when the oil is stressed over a 24 hour period.Finally Comsol Multiphysics simulation is carried out to compare to the results of the experimental results obtained in the laboratory. The results of the current as well as the resistance values obtained using the comsol simulation bears great similarity to that of the laboratory experiments.