In the present work, we carry out a finite element analysis of visco-elastic flows for the multi-mode Giesekus model at high shear rales flow. We have already proposed a new numerical scheme suitable for the analysis of visco-elastic fluids in the previous paper. It is mainly composed of two parts: the MUSCL (Monotone Upstream-centered Scheme for Conservation Law)-TVD (Total Variation Diminishing) for the numerical analysis of the constitutive equation and the GSMAC (Generalized Simplified Maker and Cell)-FEM (Finite Element Method) for the momentum equation. We apply the new scheme for the flows through the contraction plane for the multi-mode Giesekus model that considers eight relaxation modes. It shows suitable matching with experimental data at low shear rates, and we confirm that the results are stable at high shear rates.