Georgiou et al. proposed the singular finite element method (SFEM) for solving Newtonian flow problems related to singularity, such that velocity and pressure behave like r(n) and r(n-1), respectively, near the singularity, where n is a constant (0 < n < 1) and r is the radial distance from singularity in the sense of polar coordinates; and they successfully predicted several singular problems of Newtonian fluids using the SFEM. In this study we have attempted to incorporate their SFEM in the decoupled FEM associated with several numerical techniques for solving the die-swell flow of viscoelastic (Giesekus) fluids, where the singular shape functions similar to those of Georgiou et al. (1990) are used for velocity and pressure, but as for elastic stress we have approximately adopted the same shape functions as those for velocity, and we refer to this method as the SFEM(vpE); and it is found that this newly developed scheme can predict the die-swell flow of viscoelastic fluids up to We = 130; and while the SFEM (vp), which employs the singular shape functions only for velocity and pressure but a subelement scheme for elastic stress instead, fails to converge over We = 14. It is also found that the SFEM (vpE) gives more smooth and accurate results than those obtained from the ordinary FEM with less memory size.