Due to the growing demand for offshore renewable energy, the development of durable submarine power cables is critical. Submarine power cables are expected to have a service life of over 20 years. However, it has been shown that these cables suffer from water-tree flaws that progressively extend to conductors and corrode copper, which may lead to premature failure. Water treeing is caused by the of interconnection of voids (of a few nanometers) that are present in the insulator after manufacturing or formed during operation. The economic consequences of a breakdown can be drastic due to the heavy maintenance required. In the current study, the insulator is modelled as cubic unit cells containing water voids in the form of ellipsoids. The displacement field of ellipsoids is found to be dependent on its distribution in the cubic cell and on the applied electric field. Von Mises stress and effective plastic strain at the tips of the ellipsoid are found to be significant when either the relative distance between the two ellipsoids is short or the applied electric field is high. The proposed model is intended to provide insights into the ageing of cross-linked polyethylene (XPLE), which is extremely difficult to predict experimentally due to the excessive time needed to achieve coalescence of voids.