Abstract: The stress intensity factor (SIF) is an important parameter for structural fracture analysis. The conventional finite element method (FEM) with singular elements was often adopted for SIF calculation in engineering applications, in which displacement or stress components had to be used to attain the SIF at points locating along specified lines in singular domain around the crack tip. In this paper, the Williams series is modified and a Williams macro element is presented for SIF calculation on the basis of the method of finite element with generalized degrees of freedom (FEDOFs). The displacement model for FEDOFs is derived in the singular domain, based on which the SIF near the crack tip can be obtained directly. The influence of some important parameters in the Williams element on the precision of computing results is examined and discussed. The recommended values for these parameters, including the ratio factor of radial discretization, the number of radial discretizing mesh and terms of series, are given based on detailed parametric study. Examples show that the Williams element with Generalized DOFs is more convenient and accurate for SIF analysis than the conventional FEM with singular element.