A BEM with special function as the fundamental solution was proposed to solve phase change heat conduction problems encontered in the process of semiconductor technology. By applying the Gauss integration formulas and asymptotic expansion of Bessel function, the integrations of special function, were carried out effectively.Results show that, compared with the conventional FEM, the developed method Possesses the merits of less computation time and higher accuracy. The method can be extended to three dimensional case with no difficulty.