Vitrification of high level liquid waste (HLLW) after reprocessing spent fuel from nuclear power stations is one of the most important processes in nuclear fuel cycle in Japan. Numerical simulation was developed to simulate temperature, electrical potential and noble metal elements, which are included in HLLW. Material properties in high-temperature conditions were measured to introduce into the simulation code. The numerical simulations were carried out to compare with the result of mock-up melter test and to plan the mock-up test.