In this talk we shall discuss FEM simulation techniques for vis- coelastic ow with the LCR formulation for which the positive de niteness of the discrete conformation tensor is guaranteed. The strong coupling be- tween the velocity gradient and the elastic stress, which leads to a restriction for the choice of FEM approximation spaces, and the hyperbolic nature of the problem are handled with EO-FEM. A monolithic Newton multigrid ap- proach is used to allow a direct steady simulation. We validate quantitatively this approach for the well-known benchmark of ow around cylinder for two particular models namely Oldroyd-B and Giesekus.