Abstract: Stress singularity occurs at tips of cracks embedded in engineering structures under loadings. The degree of singularity can be represented by stress intensity factors. Based on Kelvin’s fundamental solutions, the spline fictitious boundary element method, combined with the use of displacement extrapolation techniques, is proposed for calculation of stress intensity factors. The key issues in the calculation, including the discretization of boundary segments and fictitious boundary elements, the adoption of fine elements and the location of approximation points, are discussed through the analysis of two typical fracture problems. The choice principles are obtained for the calculation parameters involved. The present research work lays a sound foundation for further application of the proposed method to fracture problems.