One of the major problems in electrical insulation structure is its failure while operating at normal voltage stress, which is due to electrical treeing. It is well known that this electrical tree grows progressively and damaging locally. To analyze the electrical treeing in the laboratory being not cost effective, computer simulations are used. We have here employed a known cellular automata method with new parallel processing techniques, to reduce the computation time considering the available parallel processing systems. The major advantage is that the Cellular Automata algorithm inherently exhibits parallelism-paving way for ample exploitation. Moreover, the parallelization has helped to understand various aspects of electrical treeing also in a simple way.