Effects of different boundary conditions prescribed across the boundaries of radiofrequency ablation (RFA) models of liver cancer are investigated for the case where the tumour is at the liver boundary. Ground and Robin-type conditions (electrical field) and body temperature and thermal insulation (thermal field) conditions are examined. 3D models of the human liver based on publicly-available CT images of the liver are developed. An artificial tumour is placed inside the liver at the boundary. Simulations are carried out using the finite element method. The numerical results indicated that different electrical and thermal boundary conditions led to different predictions of the electrical potential, temperature and thermal coagulation distributions. Ground and body temperature conditions presented an unnatural physical conditions around the ablation site, which results in more intense Joule heating and excessive heat loss from the tissue. This led to thermal damage volumes that are smaller than the cases when the Robin type or the thermal insulation conditions are prescribed. The present study suggests that RFA simulations in the future must take into consideration the choice of the type of electrical and thermal boundary conditions to be prescribed in the case where the tumour is located near to the liver boundary.