Abstract: An essential improvement has been made upon the stream-line finite element method proposed by Luo-Tanner. Instead of integrating a constitutive equation along the elements' boundaries as Luo-Tanner did, one can integrate the equation along the stream lines passing through the elements' Gauss points. Thus the difficulties of discontinuous velocity gradients and the stress singularity at the exit line are avoided and the amount of computation is considerably reduced. A stricter enforcement of the incompressib...