Thermal weight function (TWF) method was introduced to calculate thermal stress intensity factors (SIF) in axisymmetric thermal shock problems. TWF is independent of time. Since repeated FEM or BEM analyses for every instant are avoided by using the TWF method, the calculation procedure is greatly simplified, and the efficiency is raised to a great deal. Formulas which combine the TWF method with FEM were given for axisymmetric problems based on the stiffness matrix derivative method. Examples show good results for the present formulations.